2022
Spaces where all closed sets are α-limit sets
HANTÁKOVÁ, Jana; Samuel Joshua ROTH and Lubomír SNOHABasic 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
Article in a journal
Field of Study
10101 Pure mathematics
Country of publisher
Netherlands
Confidentiality degree
is not subject to a state or trade secret
References:
Impact factor
Impact factor: 0.600
RIV identification code
RIV/47813059:19610/22:A0000113
Organization unit
Mathematical Institute in Opava
UT WoS
000787183300004
EID Scopus
2-s2.0-85124217541
Keywords in English
alpha-Limit set; Space with enough arcs; AF-space
Tags
Tags
International impact, Reviewed
Changed: 4/3/2023 08:54, Mgr. Aleš Ryšavý
Abstract
In the original language
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.