Open maps do not preserve Whyburn property

Franco Obersnel

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 3, page 525-530
  • ISSN: 0010-2628

Abstract

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We show that a (weakly) Whyburn space X may be mapped continuously via an open map f onto a non (weakly) Whyburn space Y . This fact may happen even between topological groups X and Y , f a homomorphism, X Whyburn and Y not even weakly Whyburn.

How to cite

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Obersnel, Franco. "Open maps do not preserve Whyburn property." Commentationes Mathematicae Universitatis Carolinae 44.3 (2003): 525-530. <http://eudml.org/doc/249178>.

@article{Obersnel2003,
abstract = {We show that a (weakly) Whyburn space $X$ may be mapped continuously via an open map $f$ onto a non (weakly) Whyburn space $Y$. This fact may happen even between topological groups $X$ and $Y$, $f$ a homomorphism, $X$ Whyburn and $Y$ not even weakly Whyburn.},
author = {Obersnel, Franco},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weakly Whyburn space; open function; Whyburn space; weakly Whyburn space; open mapping; topological group; group homomorphism},
language = {eng},
number = {3},
pages = {525-530},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Open maps do not preserve Whyburn property},
url = {http://eudml.org/doc/249178},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Obersnel, Franco
TI - Open maps do not preserve Whyburn property
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 3
SP - 525
EP - 530
AB - We show that a (weakly) Whyburn space $X$ may be mapped continuously via an open map $f$ onto a non (weakly) Whyburn space $Y$. This fact may happen even between topological groups $X$ and $Y$, $f$ a homomorphism, $X$ Whyburn and $Y$ not even weakly Whyburn.
LA - eng
KW - weakly Whyburn space; open function; Whyburn space; weakly Whyburn space; open mapping; topological group; group homomorphism
UR - http://eudml.org/doc/249178
ER -

References

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  1. Dimov G.D., Isler R., Tironi G., On functions preserving almost radiality and their relations to radial and pseudoradial spaces, Comment. Math. Univ. Carolinae 28.4 (1987), 357-360. (1987) MR0928687
  2. Obersnel F., Some notes on weakly Whyburn spaces, Topology Appl., to appear. Zbl1017.54001MR1957419
  3. Pelant J., Tkachenko M.G., Tkachuk V.V., Wilson R.G., Pseudocompact Whyburn spaces need not be Fréchet, to appear on PAMS. Zbl1028.54004MR1992867
  4. Pultr A., Tozzi A., Equationally closed subframes and representation of quotient spaces, Cahiers de la Topologie et Géométrie Différentielle Categoriques 34 (1993), 167-183. (1993) Zbl0789.54008MR1239466
  5. Simon P., On accumulation points, Cahiers de la Topologie et Géométrie Différentielle Categoriques 35 (1994), 321-327. (1994) Zbl0858.54008MR1307264
  6. Tkachuk V.V., Yashenko I.V., Almost closed sets and topologies they determine, Comment. Math. Univ. Carolinae 42.2 (2001), 395-405. (2001) MR1832158

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