Weak topology and compact open topology

On fuzzy compact-open topology

The concept of fuzzy compact-open topology is introduced and some characterizations of this topology are discussed.

Compact Open Topology and Cw Homotopy Type

On Homeomorphism Groups and the Compact-Open Topology

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...

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 ...

An Elementary Counterexample in the Compact-Open Topology

We give a short proof that the space of continuous functions from [0, 1] to [0, 1] is not compact in the compact-open topology. Suppose X and Y are compact topological spaces. Let C(X, Y ) be the space of continuous functions from X to Y , and give this space the compact-open topology. An interesting problem from topology is to prove or disprove that C(X, Y ) is compact. http://dx.doi.org/10.41...