A note on condensations of function spaces onto $\sigma$-compact and analytic spaces

Mikołaj Krupski

A note on condensations of function spaces onto $\sigma$-compact and analytic spaces

General Topology 2013-12-23 v1

Authors: Mikołaj Krupski

Abstract

Modifying a construction of W. Marciszewski we prove (in ZFC) that there exists a subspace of the real line $\mathbb{R}$ , such that the realcompact space $C_p(X)$ of continuous real-valued functions on $X$ with the pointwise convergence topology does not admit a continuous bijection onto a $\sigma$ -compact space. This answers a question of Arhangel'skii.

Keywords

general topology

Cite

@article{arxiv.1312.6081,
  title  = {A note on condensations of function spaces onto $\sigma$-compact and analytic spaces},
  author = {Mikołaj Krupski},
  journal= {arXiv preprint arXiv:1312.6081},
  year   = {2013}
}

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