Fréchet-Urysohn for finite sets, II |
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Authors: | Gary Gruenhage Paul J Szeptycki |
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Institution: | a Department of Mathematics, Auburn University, Auburn, AL 36830, USA b Atkinson Faculty, York University Toronto, ON, Canada M3J 1P3 |
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Abstract: | We continue our study G. Gruenhage, P.J. Szeptycki, Fréchet Urysohn for finite sets, Topology Appl. 151 (2005) 238-259] of several variants of the property of the title. We answer a question from that paper by showing that a space defined in a natural way from a certain Hausdorff gap is a Fréchet α2 space which is not Fréchet-Urysohn for 2-point sets (FU2), and answer a question of Hrušák by showing that under MAω1, no such “gap space” is FU2. We also introduce versions of the properties which are defined in terms of “selection principles”, give examples when possible showing that the properties are distinct, and discuss relationships of these properties to convergence in product spaces, to the αi-spaces of A.V. Arhangel'skii, and to topological games. |
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Keywords: | primary 54A20 secondary 54D55 54H11 |
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