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Property \(C''\) and function spaces. (English) Zbl 0691.54007

Summary: For a Tychonoff space X, we show that each finite product of X has property \(C''\) iff \(C_ p(X)\) has countable strong fan tightness, where \(C_ p(X)\) is the function space on X with the topology of pointwise convergence.

MSC:

54C35 Function spaces in general topology
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54B10 Product spaces in general topology
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