On regular κ -bounded spaces admitting only constant continuous mappings into T
            1 spaces of pseudocharacter ≤ κ

Serhii Bardyla; Alexander Osipov

doi:10.1007/s10474-020-01082-x

On regular κ -bounded spaces admitting only constant continuous mappings into T ₁ spaces of pseudocharacter ≤ κ

Serhii Bardyla (Corresponding author)
, Alexander Osipov

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

For each cardinal κ we construct an infinite κ-bounded (and hence countably compact) regular space Rκ such that for any T1 space Y of pseudocharacter ≤κ, each continuous function f:Rκ→Y is constant. This result resolves two problems posted by Tzannes [13] and extends results of Ciesielski and Wojciechowski [4] and Herrlich [8].

Original language	English
Pages (from-to)	323–333
Number of pages	11
Journal	Acta Mathematica Hungarica
Volume	163
Issue number	1
DOIs	https://doi.org/10.1007/s10474-020-01082-x
Publication status	Published - Feb 2021

Austrian Fields of Science 2012

101013 Mathematical logic
101022 Topology

Keywords

MOORE SPACE
constant function
countably compact space
kappa-bounded space
κ-bounded space

Access to Document

10.1007/s10474-020-01082-x

Cite this

@article{882d8ac0d0094b76a3b770475dadd8a0,

title = "On regular κ -bounded spaces admitting only constant continuous mappings into T 1 spaces of pseudocharacter ≤ κ",

abstract = "For each cardinal κ we construct an infinite κ-bounded (and hence countably compact) regular space Rκ such that for any T1 space Y of pseudocharacter ≤κ, each continuous function f:Rκ→Y is constant. This result resolves two problems posted by Tzannes [13] and extends results of Ciesielski and Wojciechowski [4] and Herrlich [8].",

keywords = "MOORE SPACE, constant function, countably compact space, kappa-bounded space, κ-bounded space",

author = "Serhii Bardyla and Alexander Osipov",

note = "Publisher Copyright: {\textcopyright} 2020, Akad{\'e}miai Kiad{\'o}, Budapest, Hungary.",

year = "2021",

month = feb,

doi = "10.1007/s10474-020-01082-x",

language = "English",

volume = "163",

pages = "323–333",

journal = "Acta Mathematica Hungarica",

issn = "0236-5294",

number = "1",

}

TY - JOUR

T1 - On regular κ -bounded spaces admitting only constant continuous mappings into T 1 spaces of pseudocharacter ≤ κ

AU - Bardyla, Serhii

AU - Osipov, Alexander

PY - 2021/2

Y1 - 2021/2

N2 - For each cardinal κ we construct an infinite κ-bounded (and hence countably compact) regular space Rκ such that for any T1 space Y of pseudocharacter ≤κ, each continuous function f:Rκ→Y is constant. This result resolves two problems posted by Tzannes [13] and extends results of Ciesielski and Wojciechowski [4] and Herrlich [8].

AB - For each cardinal κ we construct an infinite κ-bounded (and hence countably compact) regular space Rκ such that for any T1 space Y of pseudocharacter ≤κ, each continuous function f:Rκ→Y is constant. This result resolves two problems posted by Tzannes [13] and extends results of Ciesielski and Wojciechowski [4] and Herrlich [8].

KW - MOORE SPACE

KW - constant function

KW - countably compact space

KW - kappa-bounded space

KW - κ-bounded space

UR - https://www.scopus.com/pages/publications/85093916840

U2 - 10.1007/s10474-020-01082-x

DO - 10.1007/s10474-020-01082-x

M3 - Article

SN - 0236-5294

VL - 163

SP - 323

EP - 333

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1

ER -