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The \(\gamma\)-open open topology for function spaces. (English) Zbl 1265.54091

Summary: We introduce the notion of \(\gamma\)-open open topology and prove some properties which the topology does possess. We also introduce the concept of convergence of nets in \(\gamma H(X)\) (where \(\gamma H(X)\) is the set of all self \(\gamma\)-homeomorphisms on a topological space \(X\)) and show when \(\gamma H(X)\) is complete.

MSC:

54C35 Function spaces in general topology
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