Some classes of topological spaces extending the class of Δ-spaces
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Some classes of topological spaces extending the class of Δ-spaces
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
1088-6826
Volume of the periodical
152
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
883-898
UT code for WoS article
001114291400001
EID of the result in the Scopus database
2-s2.0-85181562351