Extension of continuous mappings and $H_1$-retracts

Olena Karlova

doi:10.1017/S0004972708000907

Extension of continuous mappings and $H_1$-retracts

General Topology 2014-07-03 v1

Authors: Olena Karlova

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We prove that any continuous mapping $f:E\to Y$ on a completely metrizable subspace $E$ of a perfect paracompact space $X$ can be extended to a Lebesgue class one mapping $g:X\to Y$ (i.e. for every open set $V$ in $Y$ the preimage $g^{-1}(V)$ is an $F_\sigma$ -set in $X$ ) with values in an arbitrary topological space $Y$ .

Keywords

continuous mapping extension theorem Lebesgue class one $H_1$-retract completely metrizable space perfect paracompact space $F_\sigma$-set

Cite

@article{arxiv.1407.0503,
  title  = {Extension of continuous mappings and $H_1$-retracts},
  author = {Olena Karlova},
  journal= {arXiv preprint arXiv:1407.0503},
  year   = {2014}
}

Related papers

View all related →