Displaying similar documents to “Characterization of separability for L F -spaces”

On n -in-countable bases

S. A. Peregudov (2000)

Commentationes Mathematicae Universitatis Carolinae

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Some results concerning spaces with countably weakly uniform bases are generalized for spaces with n -in-countable ones.

Metrization of function spaces with the Fell topology

Hanbiao Yang (2012)

Commentationes Mathematicae Universitatis Carolinae

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For a Tychonoff space X , let ↓ C F ( X ) be the family of hypographs of all continuous maps from X to [ 0 , 1 ] endowed with the Fell topology. It is proved that X has a dense separable metrizable locally compact open subset if ↓ C F ( X ) is metrizable. Moreover, for a first-countable space X , ↓ C F ( X ) is metrizable if and only if X itself is a locally compact separable metrizable space. There exists a Tychonoff space X such that ↓ C F ( X ) is metrizable but X is not first-countable.

A note on topological groups and their remainders

Liang-Xue Peng, Yu-Feng He (2012)

Czechoslovak Mathematical Journal

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In this note we first give a summary that on property of a remainder of a non-locally compact topological group G in a compactification b G makes the remainder and the topological group G all separable and metrizable. If a non-locally compact topological group G has a compactification b G such that the remainder b G ∖ G of G belongs to 𝒫 , then G and b G ∖ G are separable and metrizable, where 𝒫 is a class of spaces which satisfies the following conditions: (1) if X ∈ 𝒫 , then every compact subset of the...

Fragmentability and compactness in C(K)-spaces

B. Cascales, G. Manjabacas, G. Vera (1998)

Studia Mathematica

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Let K be a compact Hausdorff space, C p ( K ) the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and t p ( D ) the topology in C(K) of pointwise convergence on D. It is proved that when C p ( K ) is Lindelöf the t p ( D ) -compact subsets of C(K) are fragmented by the supremum norm of C(K). As a consequence we obtain some Namioka type results and apply them to prove that if K is separable and C p ( K ) is Lindelöf, then K is metrizable if, and only if, there is a countable...