Local compactness and homeomorphisms of spaces of continuous functions
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2010), pp. 61-68
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In this paper we prove that 1) the spaces $C_p(S)$ and $C_p(T)$ of all continuous functions in the topology of pointwise convergence are not linearly homeomorphic if $S,T$ are not locally compact metrizable while the derivation set $T^{(1)}$ is compact and the derivation set $S^{(1)}$ is not; 2) the spaces $C_K(X)$ and $C_K(Y)$ of all continuous functions in the compact-open topology are not homeomorphic if $X$ and $Y$ are completely regular spaces while $X$ is locally compact and $\sigma$-compact and there is a point $y_0\in Y$ of countable character such that every neighborhood of it is not a pseudocompact.
Keywords:
spaces of all continuous functions, linear homeomorphism, homeomorphism, metrizable space, locally compact space, topology of pointwise convergence, compact-open topology.
@article{VTGU_2010_3_a7,
author = {T. E. Khmyleva and A. E. Kirienko},
title = {Local compactness and homeomorphisms of spaces of continuous functions},
journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
pages = {61--68},
year = {2010},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTGU_2010_3_a7/}
}
TY - JOUR AU - T. E. Khmyleva AU - A. E. Kirienko TI - Local compactness and homeomorphisms of spaces of continuous functions JO - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika PY - 2010 SP - 61 EP - 68 IS - 3 UR - http://geodesic.mathdoc.fr/item/VTGU_2010_3_a7/ LA - ru ID - VTGU_2010_3_a7 ER -
T. E. Khmyleva; A. E. Kirienko. Local compactness and homeomorphisms of spaces of continuous functions. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2010), pp. 61-68. http://geodesic.mathdoc.fr/item/VTGU_2010_3_a7/