J 2022

Spaces where all closed sets are α-limit sets

HANTÁKOVÁ, Jana, Samuel Joshua ROTH and Lubomír SNOHA

Basic information

Original name

Spaces where all closed sets are α-limit sets

Authors

HANTÁKOVÁ, Jana (203 Czech Republic, guarantor, belonging to the institution), Samuel Joshua ROTH (840 United States of America, belonging to the institution) and Lubomír SNOHA (703 Slovakia)

Edition

Topology and its Applications, Amsterdam, Elsevier B.V. 2022, 0166-8641

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

RIV identification code

RIV/47813059:19610/22:A0000113

Organization unit

Mathematical Institute in Opava

UT WoS

000787183300004

Keywords in English

alpha-Limit set; Space with enough arcs; AF-space

Tags

Tags

International impact, Reviewed
Změněno: 4/3/2023 08:54, Mgr. Aleš Ryšavý

Abstract

V originále

Metrizable spaces are studied in which every closed set is an α-limit set for some continuous map and some point. It is shown that this property is enjoyed by every space containing sufficiently many arcs (formalized in the notion of a space with enough arcs), though such a space need not be arcwise connected. Further it is shown that this property is not preserved by topological sums, products and continuous images and quotients. However, positive results do hold for metrizable spaces obtained by those constructions from spaces with enough arcs.