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arXiv:1207.7004 [math.GN]AbstractReferencesReviewsResources

Injections into Function Spaces over Compacta

Raushan Z. Buzyakova

Published 2012-07-30Version 1

We study the topology of X given that Cp(X) injects into Cp(Y), where Y is compact. We first show that if Cp over a GO-space (="subspace of a lineraly ordered space") injects into Cp over a compactum, then the Dedekind remainder of the GO-space is hereditarily paracompact. Also, for each ordinal tau of uncountable cofinality, we construct a continuous bijection of Cp(tau, {0,1}) onto a subgroup of Cp(tau+1, {0,1}), which is in addition a group isomorphism.

Comments: 9 pages
Categories: math.GN
Subjects: 54C35, 54C10
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