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

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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).
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/