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On some classes of compact spaces lying in \(\Sigma\)-products. (English) Zbl 0577.54014
This paper studies what the author calls a perfect class of spaces: one that contains all compact spaces and the space of natural numbers, and which is closed under continuous images, closed subspaces and countable products. The two particular perfect classes studied in the paper are the class \(P_ 1\), of all K-analytic spaces and the class \(P_ 2\) of all Lindelöf \(\Sigma\)-spaces. The main theorems characterize those compact spaces X for which \(C_ p(X)\in P_ 1(C_ p(X)\in P_ 2\), respectively), where \(C_ p(X)\) is the space of continuous real-valued functions on X with the topology of pointwise convergence. The characterizations are in terms of certain embeddings of X into \(\Sigma\)- products.
Reviewer: R.A.McCoy

MSC:
54C35 Function spaces in general topology
54D30 Compactness
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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