Connected Hausdorff subtopologies

Jack R. Porter

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 1, page 195-201
  • ISSN: 0010-2628

Abstract

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A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825–841]. A non-H-closed, Hausdorff space with countable -weight and no connected, Hausdorff subtopology is provided.

How to cite

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Porter, Jack R.. "Connected Hausdorff subtopologies." Commentationes Mathematicae Universitatis Carolinae 42.1 (2001): 195-201. <http://eudml.org/doc/248824>.

@article{Porter2001,
abstract = {A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825–841]. A non-H-closed, Hausdorff space with countable $\pi $-weight and no connected, Hausdorff subtopology is provided.},
author = {Porter, Jack R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {connected; H-closed; extensions; condensations; connected subtopology; H-closed space; countable network},
language = {eng},
number = {1},
pages = {195-201},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Connected Hausdorff subtopologies},
url = {http://eudml.org/doc/248824},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Porter, Jack R.
TI - Connected Hausdorff subtopologies
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 1
SP - 195
EP - 201
AB - A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825–841]. A non-H-closed, Hausdorff space with countable $\pi $-weight and no connected, Hausdorff subtopology is provided.
LA - eng
KW - connected; H-closed; extensions; condensations; connected subtopology; H-closed space; countable network
UR - http://eudml.org/doc/248824
ER -

References

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  1. Porter J.R., Tikoo M.L., On Katětov spaces, Trans. Amer. Math. Soc. 289 (4) (1985), 59-71. (1985) MR0779052
  2. Porter J.R., Vermeer J., Space with coarser minimal Hausdorff topologies, Canad. Math. Bull. 32.4 (1989), 425-433. (1989) 
  3. Porter J.R., Woods R.G., Extensions and Absolutes of Hausdorff Spaces, Springer-Verlag, Berlin, 1988. Zbl0652.54016MR0918341
  4. Porter J.R., Woods R.G., Subspaces of connected spaces, Topology Appl. 68 (1996), 113-131. (1996) Zbl0855.54025MR1374077
  5. Vermeer J., Private communication, 1984, . 
  6. Tkačenko M.G., Tkachuk V.V., Uspenskij V.V., Wilson R.G., In quest of weaker connected topologies, Comment. Math Univ. Carolinae 37.4 (1996), 825-841. (1996) MR1440714

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