For a Tikhonov space X we denote by Pc(X) the semilattice of all continuous pseudometrics on X. It is proved that compact Hausdorff spaces X and Y are homeomorphic if and only if there is a positive-homogeneous (or an additive) semi-lattice isomorphism T:Pc(X) → Pc(Y). A topology on Pc(X) is called admissible if it is intermediate between the compact-open and pointwise topologies on Pc(X). Another result states that Tikhonov spaces X and Y are homeomorphic if and only if there exists a positive-homogeneous (or an additive) semi-lattice homeomorphism , where are admissible topologies on Pc(X) and Pc(Y).
@article{bwmeta1.element.bwnjournal-article-smv116i3p303bwm,
author = {Taras Banakh},
title = {Sur la caract\'erisation topologique des compacts \`a l'aide des demi-treillis des pseudom\'etriques continues},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {303-310},
language = {fr},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p303bwm}
}
Banakh, Taras. Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues. Studia Mathematica, Tome 113 (1995) pp. 303-310. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p303bwm/
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