Geodesic
A construction of a Fréchet-Urysohn space, and some convergence concepts
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 99-112 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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).
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 
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     title = {A construction of a {Fr\'echet-Urysohn} space, and some convergence concepts},
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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/