On homeomorphisms of function spaces over products with compacta. (English) Zbl 1537.54013

Buzyakova, Raushan

Rocky Mt. J. Math. 52, No. 6, 2003-2007 (2022).

Summary: We show that if \(C_p(X\times Z)\) is homeomorphic to \(C_p(Y\times Z)\), where \(Z\) is compact, and \(X\) and \(Y\) are of countable netweight, then \(C_p(X\times M)\) is homeomorphic to \(C_p(Y\times M)\) for some metric compactum \(M\). Spaces \(X, Y, Z\), and \(M\) are assumed nonempty.

MSC:

54C35	Function spaces in general topology
54B10	Product spaces in general topology
54C10	Special maps on topological spaces (open, closed, perfect, etc.)

Keywords:

function spaces in the topology of point-wise convergence; product spaces; quotient map; homeomorphism; countable netweight

References:

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