Displaying similar documents to “A note on maximally resolvable spaces.”

A Hilbert cube compactification of the function space with the compact-open topology

Atsushi Kogasaka, Katsuro Sakai (2009)

Open Mathematics

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Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification C ¯ (X) of C(X) such that the pair ( C ¯ (X), C(X)) is homeomorphic to (Q,...

On the cardinality of n-Urysohn and n-Hausdorff spaces

Maddalena Bonanzinga, Maria Cuzzupé, Bruno Pansera (2014)

Open Mathematics

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Two variations of Arhangelskii’s inequality X ⩽ 2 χ ( X ) - L ( X ) for Hausdorff X [Arhangel’skii A.V., The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR, 1969, 187, 967–970 (in Russian)] given in [Stavrova D.N., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc., 2000, 25(Summer), 333–343] are extended to the classes with finite Urysohn number or finite Hausdorff number.