The κ-Fréchet--Urysohn property for locally convex spaces

2018/12/25 by Gabriyelyan, S.
#46A03 #46A08 #54C35 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · doi:10.48550/arxiv.1812.10166

Abstract

A topological space X is κ-Fréchet--Urysohn if for every open subset U of X and every x∈ U there exists a sequence in U converging to x. We prove that every κ-Fréchet--Urysohn Tychonoff space X is Ascoli. We apply this statement and some of known results to characterize the κ-Fréchet--Urysohn property in various important classes of locally convex spaces. In particular, answering a question posed in [7] we obtain that C_p(X) is Ascoli iff X has the property (κ).

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