Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues

Taras Banakh

Studia Mathematica (1995)

  • Volume: 116, Issue: 3, page 303-310
  • ISSN: 0039-3223

Abstract

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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 T : ( P c ( X ) , τ X ) → ( P c ( Y ) , τ Y ) , where τ X , τ Y are admissible topologies on Pc(X) and Pc(Y).

How to cite

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Banakh, Taras. "Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues." Studia Mathematica 116.3 (1995): 303-310. <http://eudml.org/doc/216237>.

@article{Banakh1995,
author = {Banakh, Taras},
journal = {Studia Mathematica},
keywords = {Tikhonov space; semilattice of all continuous pseudometrics; admissible topologies},
language = {fre},
number = {3},
pages = {303-310},
title = {Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues},
url = {http://eudml.org/doc/216237},
volume = {116},
year = {1995},
}

TY - JOUR
AU - Banakh, Taras
TI - Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues
JO - Studia Mathematica
PY - 1995
VL - 116
IS - 3
SP - 303
EP - 310
LA - fre
KW - Tikhonov space; semilattice of all continuous pseudometrics; admissible topologies
UR - http://eudml.org/doc/216237
ER -

References

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  1. [Ba] S. Banach, Théorie des opérations linéaires, Warszawa, 1932. Zbl0005.20901
  2. [En] R. Engelking, General Topology, PWN, Warszawa, 1977. 
  3. [GK] I. M. Gelfand and A. N. Kolmogoroff [A. N. Kolmogorov], On rings of continuous functions on topological spaces, Dokl. Akad. Nauk SSSR 22 (1939), 11-15. Zbl65.0500.03
  4. [Ka] I. Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617-623. Zbl0031.21902
  5. [Se] Z. Semadeni, Banach Spaces of Continuous Functions, PWN, Warszawa, 1971. 
  6. [Sh] T. Shirota, A generalization of a theorem of I. Kaplansky, Osaka Math. J. 4 (1952), 121-132. Zbl0048.08902

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