Spaces where all closed sets are α-limit sets

@article{65261,
   author = {Hantáková, Jana and Roth, Samuel Joshua and Snoha, Lubomír},
   article_location = {Amsterdam},
   article_number = {april},
   doi = {http://dx.doi.org/10.1016/j.topol.2022.108035},
   keywords = {alpha-Limit set; Space with enough arcs; AF-space},
   language = {eng},
   issn = {0166-8641},
   journal = {Topology and its Applications},
   title = {Spaces where all closed sets are α-limit sets},
   url = {https://www.sciencedirect.com/science/article/pii/S0166864122000372},
   volume = {310},
   year = {2022}
}

TY  - JOUR
ID  - 65261
AU  - Hantáková, Jana - Roth, Samuel Joshua - Snoha, Lubomír
PY  - 2022
TI  - Spaces where all closed sets are α-limit sets
JF  - Topology and its Applications
VL  - 310
IS  - april
SP  - "108035-1"-"108035-16"
EP  - "108035-1"-"108035-16"
PB  - Elsevier B.V.
SN  - 01668641
KW  - alpha-Limit set
KW  - Space with enough arcs
KW  - AF-space
UR  - https://www.sciencedirect.com/science/article/pii/S0166864122000372
N2  - 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.
ER  - 

HANTÁKOVÁ, Jana, Samuel Joshua ROTH and Lubomír SNOHA. Spaces where all closed sets are α-limit sets. \textit{Topology and its Applications}. Amsterdam: Elsevier B.V., 2022, vol.~310, april, p.~''108035-1''-''108035-16'', 16 pp. ISSN~0166-8641. Available from: https://dx.doi.org/10.1016/j.topol.2022.108035.