H-closed and extremally disconnected Hausdorff spaces

J. Mioduszewski; L. Rudolf

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1969

Abstract

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CONTENTSIntroduction.......................................................................................................................................................... 5I. PRELIMINARIES.............................................................................................................................................. 7§ 1. The closures of open subsets in r. o.-equivalent topologies............................................................. 7§ 2. The r. o.-maximal topologies.................................................................................................................... 9§ 3. The H-closed maximal spaces................................................................................................................ 10§ 4. R. o.-equivalence of extensions............................................................................................................... 10§ 5. 0-continuous maps.................................................................................................................................... 11§ 6. The Henriksen-Jerison and skeletal maps........................................................................................... 13II. H-CLOSED EXTENSIONS OF HAUSDORFF SPACES.................................................................................... 14§ 1. The set of 77-closed extensions of given Hausdorff space............................................................... 145 2. Proper maps................................................................................................................................................ 16§ 3. Decompositions of proper maps............................................................................................................ 18§ 4. An application to IT-closed extensions................................................................................................... 19§ 5. The case of compact-like spaces........................................................................................................... 22§ 6. The case of minimal Hausdorff spaces................................................................................................. 25III. EXTREMALLY DISCONNECTED RESOLUTIONS OF HAUSDORFF SPACES................................. 26§ 1. The set of irreducible maps onto a given Hausdorff space X............................................................ 26§ 2. R. o.-minimal irreducible maps............................................................................................................... 30§ 3. Extremally disconnected resolutions...................................................................................................... 31IV. COMMUTATION OF H-CLOSED EXTENSIONS AND E. D. RESOLUTIONS...................................... 35§ 1. Commutativity in a pullback diagram...................................................................................................... 35§ 2. Commutativity in a pushout diagram ..................................................................................................... 37V. PROJECTIVE AND INJECTIVE HAUSDORFF SPACES......................................................................... 39§ 1. H-closed projective spaces. A definition and motivations.................................................................. 41§ 2. The case of compact-like spaces........................................................................................................... 42§ 3. Projectiveness for arbitrary H-closed spaces....................................................................................... 44§ 4. Projectiveness for arbitrary Hausdorff spaces...................................................................................... 45§ 5. Injective extremally disconnected spaces............................................................................................. 46§ 6. Injective Hausdorff spaces....................................................................................................................... 48Bibliography......................................................................................................................................................... 51

How to cite

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J. Mioduszewski, and L. Rudolf. H-closed and extremally disconnected Hausdorff spaces. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1969. <http://eudml.org/doc/268441>.

@book{J1969,
abstract = {CONTENTSIntroduction.......................................................................................................................................................... 5I. PRELIMINARIES.............................................................................................................................................. 7§ 1. The closures of open subsets in r. o.-equivalent topologies............................................................. 7§ 2. The r. o.-maximal topologies.................................................................................................................... 9§ 3. The H-closed maximal spaces................................................................................................................ 10§ 4. R. o.-equivalence of extensions............................................................................................................... 10§ 5. 0-continuous maps.................................................................................................................................... 11§ 6. The Henriksen-Jerison and skeletal maps........................................................................................... 13II. H-CLOSED EXTENSIONS OF HAUSDORFF SPACES.................................................................................... 14§ 1. The set of 77-closed extensions of given Hausdorff space............................................................... 145 2. Proper maps................................................................................................................................................ 16§ 3. Decompositions of proper maps............................................................................................................ 18§ 4. An application to IT-closed extensions................................................................................................... 19§ 5. The case of compact-like spaces........................................................................................................... 22§ 6. The case of minimal Hausdorff spaces................................................................................................. 25III. EXTREMALLY DISCONNECTED RESOLUTIONS OF HAUSDORFF SPACES................................. 26§ 1. The set of irreducible maps onto a given Hausdorff space X............................................................ 26§ 2. R. o.-minimal irreducible maps............................................................................................................... 30§ 3. Extremally disconnected resolutions...................................................................................................... 31IV. COMMUTATION OF H-CLOSED EXTENSIONS AND E. D. RESOLUTIONS...................................... 35§ 1. Commutativity in a pullback diagram...................................................................................................... 35§ 2. Commutativity in a pushout diagram ..................................................................................................... 37V. PROJECTIVE AND INJECTIVE HAUSDORFF SPACES......................................................................... 39§ 1. H-closed projective spaces. A definition and motivations.................................................................. 41§ 2. The case of compact-like spaces........................................................................................................... 42§ 3. Projectiveness for arbitrary H-closed spaces....................................................................................... 44§ 4. Projectiveness for arbitrary Hausdorff spaces...................................................................................... 45§ 5. Injective extremally disconnected spaces............................................................................................. 46§ 6. Injective Hausdorff spaces....................................................................................................................... 48Bibliography......................................................................................................................................................... 51},
author = {J. Mioduszewski, L. Rudolf},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {H-closed and extremally disconnected Hausdorff spaces},
url = {http://eudml.org/doc/268441},
year = {1969},
}

TY - BOOK
AU - J. Mioduszewski
AU - L. Rudolf
TI - H-closed and extremally disconnected Hausdorff spaces
PY - 1969
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction.......................................................................................................................................................... 5I. PRELIMINARIES.............................................................................................................................................. 7§ 1. The closures of open subsets in r. o.-equivalent topologies............................................................. 7§ 2. The r. o.-maximal topologies.................................................................................................................... 9§ 3. The H-closed maximal spaces................................................................................................................ 10§ 4. R. o.-equivalence of extensions............................................................................................................... 10§ 5. 0-continuous maps.................................................................................................................................... 11§ 6. The Henriksen-Jerison and skeletal maps........................................................................................... 13II. H-CLOSED EXTENSIONS OF HAUSDORFF SPACES.................................................................................... 14§ 1. The set of 77-closed extensions of given Hausdorff space............................................................... 145 2. Proper maps................................................................................................................................................ 16§ 3. Decompositions of proper maps............................................................................................................ 18§ 4. An application to IT-closed extensions................................................................................................... 19§ 5. The case of compact-like spaces........................................................................................................... 22§ 6. The case of minimal Hausdorff spaces................................................................................................. 25III. EXTREMALLY DISCONNECTED RESOLUTIONS OF HAUSDORFF SPACES................................. 26§ 1. The set of irreducible maps onto a given Hausdorff space X............................................................ 26§ 2. R. o.-minimal irreducible maps............................................................................................................... 30§ 3. Extremally disconnected resolutions...................................................................................................... 31IV. COMMUTATION OF H-CLOSED EXTENSIONS AND E. D. RESOLUTIONS...................................... 35§ 1. Commutativity in a pullback diagram...................................................................................................... 35§ 2. Commutativity in a pushout diagram ..................................................................................................... 37V. PROJECTIVE AND INJECTIVE HAUSDORFF SPACES......................................................................... 39§ 1. H-closed projective spaces. A definition and motivations.................................................................. 41§ 2. The case of compact-like spaces........................................................................................................... 42§ 3. Projectiveness for arbitrary H-closed spaces....................................................................................... 44§ 4. Projectiveness for arbitrary Hausdorff spaces...................................................................................... 45§ 5. Injective extremally disconnected spaces............................................................................................. 46§ 6. Injective Hausdorff spaces....................................................................................................................... 48Bibliography......................................................................................................................................................... 51
LA - eng
UR - http://eudml.org/doc/268441
ER -

Citations in EuDML Documents

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  1. Taras Banakh, Andrzej Kucharski, Marta Martynenko, A spectral characterization of skeletal maps
  2. A. Bella, A. Błaszczyk, A. Szymański, On absolute retracts of ω*
  3. Melvin Henriksen, Jorge Martinez, Grant R. Woods, Spaces X in which all prime z -ideals of C ( X ) are minimal or maximal
  4. Bernhard Banaschewski, Aleš Pultr, Booleanization of uniform frames
  5. Andrzej Kucharski, Szymon Plewik, Vesko Valov, Skeletally Dugundji spaces
  6. B. Banaschewski, A. Pultr, Booleanization
  7. H. L. Bentley, Horst Herrlich, Completion as reflection
  8. Dragan S. Janković, Ch. Konstadilaki-Savvopoulou, On α -continuous functions

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