Homological methods in fixed-point theory of multi-valued maps

Lech Górniewicz

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1976

Abstract

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CONTENTS  Introduction................................................................. 5I. HOMOLOGY  1. Preliminaries............................................................. 7  2. Maps in spaces of finite type............................................. 9  3. The Čech homology functor with compact carriers........................... 11  4. Vietoris maps............................................................. 13  5. Homology of open subsets of Euclidean spaces.............................. 14II. THE LEFSCHETZ NUMBER  1. The (ordinary) Lefschetz number........................................... 18  2. The generalized Lefschetz number.......................................... 20III. MULTI-VALUED MAPS  1. Upper semi-continuous and compact multi-valued mapB....................... 24  2. Admissible maps........................................................... 26  3. Homotopy and selectors.................................................... 9  4. Lefschetz maps............................................................ 30IV. ANB-s, AANR-B and w-AANB-s  1. ANR-s..................................................................... 32  2. Approximation Theorem..................................................... 33  3. AANR-B.................................................................... 34  4. w-AANR-s.................................................................. 36V. THE LEFSCHETZ FIXED-POINT THEOREM  1. The index of coincidence.................................................. 37  2. The Lefschetz Fixed-Point Theorem for open subsets in R n ............... 40  3. The Lefschetz Fixed-Point Theorem for AANR-s.............................. 41  4. Neighbourhood fixed-point property........................................ 45  5. The Lefschetz Fixed-Point Theorem for w-AANR-s............................ 46  6. Two consequences of the Lefschetz Fixed-Point Theorem..................... 47VI. FIXED-POINT PROPERTY OP THE TYCHONOFF CUBE  1. Almost fixed points....................................................... 51  2. Fixed-point property for infinite products................................ 51

How to cite

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Lech Górniewicz. Homological methods in fixed-point theory of multi-valued maps. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1976. <http://eudml.org/doc/268399>.

@book{LechGórniewicz1976,
abstract = {CONTENTS  Introduction................................................................. 5I. HOMOLOGY  1. Preliminaries............................................................. 7  2. Maps in spaces of finite type............................................. 9  3. The Čech homology functor with compact carriers........................... 11  4. Vietoris maps............................................................. 13  5. Homology of open subsets of Euclidean spaces.............................. 14II. THE LEFSCHETZ NUMBER  1. The (ordinary) Lefschetz number........................................... 18  2. The generalized Lefschetz number.......................................... 20III. MULTI-VALUED MAPS  1. Upper semi-continuous and compact multi-valued mapB....................... 24  2. Admissible maps........................................................... 26  3. Homotopy and selectors.................................................... 9  4. Lefschetz maps............................................................ 30IV. ANB-s, AANR-B and w-AANB-s  1. ANR-s..................................................................... 32  2. Approximation Theorem..................................................... 33  3. AANR-B.................................................................... 34  4. w-AANR-s.................................................................. 36V. THE LEFSCHETZ FIXED-POINT THEOREM  1. The index of coincidence.................................................. 37  2. The Lefschetz Fixed-Point Theorem for open subsets in $R^n$............... 40  3. The Lefschetz Fixed-Point Theorem for AANR-s.............................. 41  4. Neighbourhood fixed-point property........................................ 45  5. The Lefschetz Fixed-Point Theorem for w-AANR-s............................ 46  6. Two consequences of the Lefschetz Fixed-Point Theorem..................... 47VI. FIXED-POINT PROPERTY OP THE TYCHONOFF CUBE  1. Almost fixed points....................................................... 51  2. Fixed-point property for infinite products................................ 51},
author = {Lech Górniewicz},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Homological methods in fixed-point theory of multi-valued maps},
url = {http://eudml.org/doc/268399},
year = {1976},
}

TY - BOOK
AU - Lech Górniewicz
TI - Homological methods in fixed-point theory of multi-valued maps
PY - 1976
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTS  Introduction................................................................. 5I. HOMOLOGY  1. Preliminaries............................................................. 7  2. Maps in spaces of finite type............................................. 9  3. The Čech homology functor with compact carriers........................... 11  4. Vietoris maps............................................................. 13  5. Homology of open subsets of Euclidean spaces.............................. 14II. THE LEFSCHETZ NUMBER  1. The (ordinary) Lefschetz number........................................... 18  2. The generalized Lefschetz number.......................................... 20III. MULTI-VALUED MAPS  1. Upper semi-continuous and compact multi-valued mapB....................... 24  2. Admissible maps........................................................... 26  3. Homotopy and selectors.................................................... 9  4. Lefschetz maps............................................................ 30IV. ANB-s, AANR-B and w-AANB-s  1. ANR-s..................................................................... 32  2. Approximation Theorem..................................................... 33  3. AANR-B.................................................................... 34  4. w-AANR-s.................................................................. 36V. THE LEFSCHETZ FIXED-POINT THEOREM  1. The index of coincidence.................................................. 37  2. The Lefschetz Fixed-Point Theorem for open subsets in $R^n$............... 40  3. The Lefschetz Fixed-Point Theorem for AANR-s.............................. 41  4. Neighbourhood fixed-point property........................................ 45  5. The Lefschetz Fixed-Point Theorem for w-AANR-s............................ 46  6. Two consequences of the Lefschetz Fixed-Point Theorem..................... 47VI. FIXED-POINT PROPERTY OP THE TYCHONOFF CUBE  1. Almost fixed points....................................................... 51  2. Fixed-point property for infinite products................................ 51
LA - eng
UR - http://eudml.org/doc/268399
ER -

Citations in EuDML Documents

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  1. Adam Idzik, Borsuk-Ulam type theorems
  2. David Richeson, Connection matrix pairs
  3. Tomasz Kaczynski, Conley index for set-valued maps: from theory to computation
  4. Marian Mrozek, From the theorem of Ważewski to computer assisted proofs in dynamics
  5. Dorota Gabor, The coincidence index for fundamentally contractible multivalued maps with nonconvex values
  6. Lech Górniewicz, Danuta Rozpłoch-Nowakowska, On the Schauder fixed point theorem
  7. Peter Saveliev, A Lefschetz-type coincidence theorem
  8. Liang-Ju Chu, Ching-Yan Lin, New versions on Nikaidô's coincidence theorem
  9. Lech Górniewicz, On the Lefschetz fixed point theorem
  10. Mircea Balaj, Admissible maps, intersection results, coincidence theorems

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