# 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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