On condensations of $C_{p}$-spaces onto compacta

A. V. Arhangel'skii
2000 Proceedings of the American Mathematical Society  
A condensation is a one-to-one onto mapping. It is established that, for each σ-compact metrizable space X, the space Cp(X) of real-valued continuous functions on X in the topology of pointwise convergence condenses onto a metrizable compactum. Note that not every Tychonoff space condenses onto a compactum.
doi:10.1090/s0002-9939-00-05758-0 fatcat:ehtpquygrvfrxo2aqhorjzofiq