HANTÁKOVÁ, Jana, Samuel Joshua ROTH and Lubomír SNOHA. Spaces where all closed sets are α-limit sets. 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. |
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@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.
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