Geodesic
A construction of a Fréchet-Urysohn space, and some convergence concepts
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 99-112.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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).
Classification : 54D20, 54G20, 54J99
Keywords: first-countable; Fréchet-Urysohn; countably compact; closure-sensor; topological group; strong FU-sensor; pseudoopen mapping; side-base; $\omega $-Fréchet-Urysohn space 
@article{CMUC_2010__51_1_a8,
     author = {Arhangel'skii, A. V.},
     title = {A construction of a {Fr\'echet-Urysohn} space, and some convergence concepts},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {99--112},
     publisher = {mathdoc},
     volume = {51},
     number = {1},
     year = {2010},
     mrnumber = {2666083},
     zbl = {1224.54055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a8/}
}
TY  - JOUR
AU  - Arhangel'skii, A. V.
TI  - A construction of a Fréchet-Urysohn space, and some convergence concepts
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2010
SP  - 99
EP  - 112
VL  - 51
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a8/
LA  - en
ID  - CMUC_2010__51_1_a8
ER  - 
%0 Journal Article
%A Arhangel'skii, A. V.
%T A construction of a Fréchet-Urysohn space, and some convergence concepts
%J Commentationes Mathematicae Universitatis Carolinae
%D 2010
%P 99-112
%V 51
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a8/
%G en
%F CMUC_2010__51_1_a8
Arhangel'skii, A. V. A construction of a Fréchet-Urysohn space, and some convergence concepts. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 99-112. http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a8/