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

• Autorzy: Taras Banakh
• Języki publikacji: FR EN

Abstrakty

EN

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 $T:(Pc(X),τ_X) → (Pc(Y),τ_Y)$, where $τ_X,τ_Y$ are admissible topologies on Pc(X) and Pc(Y).

Kategorie tematyczne

• 54C35: Function spaces
• 06A12: Semilattices
• 54F65: Topological characterizations of particular spaces
• 54H12: Topological lattices, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 116
• Numer: 3
• Strony: 303-310

Daty

wydano

1995

otrzymano

1995-05-17

Twórcy

autor

Taras Banakh

• Faculté de Mathématiques, Université de Lviv, Universytetska 1, Lviv, 290602, Ukraine

Bibliografia

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• [Ka] I. Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617-623.
• [Se] Z. Semadeni, Banach Spaces of Continuous Functions, PWN, Warszawa, 1971.
• [Sh] T. Shirota, A generalization of a theorem of I. Kaplansky, Osaka Math. J. 4 (1952), 121-132.