Homeomorphisms between function spaces
Keywords:Homeomorphism, \(t_H\)-embedded, \(t_H\)-equivalent, point-open topology, open-point topology, bi-point-open topology
Given a space \(X\) and topological group \(H\), \(C(X,H)\) denotes the set of all continuous functions from a space \(X\) to a topological group \(H\). For a subset \(A\) of a space \(X\), \(X/A\)Â denotes the quotient space with quotient topology obtained from $X$ by identifying $A$ to a point. We study some homeomorphisms between \(C(X,H)\) and \(C(Y,H)\) for different \(X\) and \(Y\) under the point-open topology, open-point topology and bi-point-open topology.
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