Some upper bounds for density of function spaces |
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Authors: | Süleyman Önal Çetin Vural |
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Institution: | a Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey b Gazi Universitesi, Fen-Edebiyat Fakultesi, Matematik Bolumu, 06500 Ankara, Turkey |
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Abstract: | Let Cα(X,Y) be the set of all continuous functions from X to Y endowed with the set-open topology where α is a hereditarily closed, compact network on X which is closed under finite unions. We proved that the density of the space Cα(X,Y) is at most iw(X)⋅d(Y) where iw(X) denotes the i-weight of the Tychonoff space X, and d(Y) denotes the density of the space Y when Y is an equiconnected space with equiconnecting function Ψ, and Y has a base consists of Ψ-convex subsets of Y. We also prove that the equiconnectedness of the space Y cannot be replaced with pathwise connectedness of Y. In fact, it is shown that for each infinite cardinal κ, there is a pathwise connected space Y such that π-weight of Y is κ, but Souslin number of the space Ck(0,1],Y) is κ2. |
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Keywords: | 54C05 54C35 54D65 |
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