The C-compact-open topology on function spaces
نویسندگان
چکیده
منابع مشابه
Sequential Properties of Function Spaces with the Compact-open Topology
Let M be the countably infinite metric fan. We show that Ck(M, 2) is sequential and contains a closed copy of Arens space S2. It follows that if X is metrizable but not locally compact, then Ck(X) contains a closed copy of S2, and hence does not have the property AP. We also show that, for any zero-dimensional Polish space X, Ck(X, 2) is sequential if and only if X is either locally compact or ...
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If X is a topological space, then we let H(X) denote the group of autohomeomorphisms of X equipped with the compact-open topology. For subsets A and B of X we define [A, B] = {h ∈ H(X) : h(A) ⊂ B}, and we recall that the topology on H(X) is generated by the subbasis SX = {[K , O] : K compact, O open in X}. If X is a compact Hausdorff space, then H(X) is a topological group, that is, composition...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2012
ISSN: 0166-8641
DOI: 10.1016/j.topol.2012.05.018