A construction of a Fréchet-Urysohn space, and some convergence concepts
Commentationes Mathematicae Universitatis Carolinae (2010)
- Volume: 51, Issue: 1, page 99-112
- ISSN: 0010-2628
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topArhangel'skii, Aleksander V.. "A construction of a Fréchet-Urysohn space, and some convergence concepts." Commentationes Mathematicae Universitatis Carolinae 51.1 (2010): 99-112. <http://eudml.org/doc/37741>.
@article{Arhangelskii2010,
abstract = {Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen mapping. On the other hand, if a topological group $G$ is an image of a separable metrizable space under a pseudoopen continuous mapping, then $G$ is metrizable (Theorem 5.6). Several other applications of the techniques developed below to the study of pseudoopen mappings and intersections of topologies are given (see Theorem 5.17).},
author = {Arhangel'skii, Aleksander V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {first-countable; Fréchet-Urysohn; countably compact; closure-sensor; topological group; strong FU-sensor; pseudoopen mapping; side-base; $\omega $-Fréchet-Urysohn space; first countable space; Fréchet-Urysohn space; closure-sensor; side-base; -Fréchet-Urysohn space},
language = {eng},
number = {1},
pages = {99-112},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A construction of a Fréchet-Urysohn space, and some convergence concepts},
url = {http://eudml.org/doc/37741},
volume = {51},
year = {2010},
}
TY - JOUR
AU - Arhangel'skii, Aleksander V.
TI - A construction of a Fréchet-Urysohn space, and some convergence concepts
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 1
SP - 99
EP - 112
AB - Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen mapping. On the other hand, if a topological group $G$ is an image of a separable metrizable space under a pseudoopen continuous mapping, then $G$ is metrizable (Theorem 5.6). Several other applications of the techniques developed below to the study of pseudoopen mappings and intersections of topologies are given (see Theorem 5.17).
LA - eng
KW - first-countable; Fréchet-Urysohn; countably compact; closure-sensor; topological group; strong FU-sensor; pseudoopen mapping; side-base; $\omega $-Fréchet-Urysohn space; first countable space; Fréchet-Urysohn space; closure-sensor; side-base; -Fréchet-Urysohn space
UR - http://eudml.org/doc/37741
ER -
References
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