Some upper bounds for density of function spaces

Date

2009-05-01

Author

Önal, Süleyman

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Let C-alpha(X, Y) be the set of all continuous functions from X to Y endowed with the set-open topology where alpha is a hereditarily closed, compact network on X which is closed Under finite unions. We proved that the density of the space C-alpha(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 psi, and Y has a base consists of psi-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 kappa, there is a pathwise connected space Y Such that pi-weight of Y is kappa, but Souslin number of the Space C-kappa(vertical bar 0, 1 vertical bar, Y) is 2(kappa).

Subject Keywords

Geometry and Topology

URI

https://hdl.handle.net/11511/40090

Journal

TOPOLOGY AND ITS APPLICATIONS

DOI

https://doi.org/10.1016/j.topol.2009.01.007

Collections

Department of Mathematics, Article

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Citation Formats

S. Önal, “Some upper bounds for density of function spaces,” TOPOLOGY AND ITS APPLICATIONS, pp. 1630–1635, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40090.