Injections into Function Spaces over Compacta
General Topology
2012-07-31 v1
Abstract
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.
Cite
@article{arxiv.1207.7004,
title = {Injections into Function Spaces over Compacta},
author = {Raushan Z. Buzyakova},
journal= {arXiv preprint arXiv:1207.7004},
year = {2012}
}
Comments
9 pages