K-analytic and Analytic Spaces Cp(X)
This chapter deals with K-analytic and analytic spaces C p (X). Some results due to Talagrand, Tkachuk, Velichko and Canela are presented. A remarkable theorem of Christensen stating that a metrizable and separable space X is σ-compact if and only if C p (X) is analytic is proved. We show that the analyticity of C p (X) for any X implies that X is σ-compact (Calbrix’s theorem). We show that C p (X) is K-analytic-framed in ℝ X if and only if C p (X) admits a bounded resolution. We also gather several equivalent conditions for spaces C p (X) to be Lindelöf spaces over locally compact groups X.
KeywordsTopological Space Compact Subset Compact Group Compact Space Closed Subspace
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