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Sobrification of partially ordered sets.

R.E. Hoffmann (1979)

Semigroup forum

Some Baire category type theorems for $U (ω_{1})$

Andrzej Szymański (1979)

Commentationes Mathematicae Universitatis Carolinae

Some order theoretic characterizations of the 3-cell

E. D. Tymchatyn (1972)

Colloquium Mathematicae

Spaces of continuous functions, box products and almost- $ω$ -resolvable spaces

Angel Tamariz-Mascarúa, H. Villegas-Rodríguez (2002)

Commentationes Mathematicae Universitatis Carolinae

A dense-in-itself space $X$ is called $C_{□}$ -discrete if the space of real continuous functions on $X$ with its box topology, $C_{□} (X)$ , is a discrete space. A space $X$ is called almost- $ω$ -resolvable provided that $X$ is the union of a countable increasing family of subsets each of them with an empty interior. We analyze these classes of spaces by determining their relations with $κ$ -resolvable and almost resolvable spaces. We prove that every almost- $ω$ -resolvable space is $C_{□}$ -discrete, and that these classes coincide in...

Strongly paracompact metrizable spaces

Valentin Gutev (2016)

Colloquium Mathematicae

Strongly paracompact metrizable spaces are characterized in terms of special S-maps onto metrizable non-Archimedean spaces. A similar characterization of strongly metrizable spaces is obtained as well. The approach is based on a sieve-construction of "metric"-continuous pseudo-sections of lower semicontinuous mappings.

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

Taras Banakh (1995)

Studia Mathematica

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...