Some upper bounds for density of function spaces

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).


Some cardinal invariants on the space C-alpha (X, Y)
Onal, S; Vural, C (Elsevier BV, 2005-05-14)
Let C-alpha (X, Y) be the set of all continuous functions from X to Y endowed with the set-open topology where a is a hereditarily closed, compact network on X such that closed under finite unions. We define two properties (E1) and (E2) on the triple (alpha, X, Y) which yield new equalities and inequalities between some cardinal invariants on C-alpha (X, Y) and some cardinal invariants on the spaces X, Y such as:
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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: