Some classes of topological spaces extending the class of Δ-spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00580514" target="_blank" >RIV/67985840:_____/24:00580514 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1090/proc/16661" target="_blank" >https://doi.org/10.1090/proc/16661</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/proc/16661" target="_blank" >10.1090/proc/16661</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Some classes of topological spaces extending the class of Δ-spaces

Popis výsledku v původním jazyce

A study of the class Delta consisting of topological Delta-spaces was originated by Jerzy Kakol and Arkady Leiderman [Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 86-99, Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 267-280]. The main purpose of this paper is to introduce and investigate new classes Delta(2) subset of Delta(1) properly containing Delta.nWe observe that for every first-countable X the following equivalences hold: X is an element of Delta(1) iff X is an element of Delta(2) iff each countable subset of X is G(delta). Thus, new proposed concepts provide a natural extension of the family of all lambda-sets beyond the separable metrizable spaces.nWe prove that (1) A pseudocompact space X belongs to the class Delta(1) iff countable subsets of X are scattered. (2) Every regular scattered space belongs to the class Delta(2).nWe investigate whether the classes Delta(1) and Delta(2) are invariant under the basic topological operations. Similarly to Delta, both classes Delta(1) and Delta(2) are invariant under the operation of taking countable unions of closed subspaces. In contrast to Delta, they are not preserved by closed continuous images.nLet Y be l-dominated by X, i.e. C-p(X) admits a continuous linear map onto C-p(Y). We show that Y is an element of Delta(1) whenever X is an element of Delta(1). Moreover, we establish that if Y is l-dominated by a compact scattered space X, then Y is a pseudocompact space such that its Stone-Cech compactification beta Y is scattered.

Název v anglickém jazyce

Some classes of topological spaces extending the class of Δ-spaces

Popis výsledku anglicky

A study of the class Delta consisting of topological Delta-spaces was originated by Jerzy Kakol and Arkady Leiderman [Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 86-99, Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 267-280]. The main purpose of this paper is to introduce and investigate new classes Delta(2) subset of Delta(1) properly containing Delta.nWe observe that for every first-countable X the following equivalences hold: X is an element of Delta(1) iff X is an element of Delta(2) iff each countable subset of X is G(delta). Thus, new proposed concepts provide a natural extension of the family of all lambda-sets beyond the separable metrizable spaces.nWe prove that (1) A pseudocompact space X belongs to the class Delta(1) iff countable subsets of X are scattered. (2) Every regular scattered space belongs to the class Delta(2).nWe investigate whether the classes Delta(1) and Delta(2) are invariant under the basic topological operations. Similarly to Delta, both classes Delta(1) and Delta(2) are invariant under the operation of taking countable unions of closed subspaces. In contrast to Delta, they are not preserved by closed continuous images.nLet Y be l-dominated by X, i.e. C-p(X) admits a continuous linear map onto C-p(Y). We show that Y is an element of Delta(1) whenever X is an element of Delta(1). Moreover, we establish that if Y is l-dominated by a compact scattered space X, then Y is a pseudocompact space such that its Stone-Cech compactification beta Y is scattered.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Proceedings of the American Mathematical Society

ISSN

0002-9939

e-ISSN

1088-6826

Svazek periodika

152

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

883-898

Kód UT WoS článku

001114291400001

EID výsledku v databázi Scopus

2-s2.0-85181562351