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Coincidence of Vietoris and Wijsman Topologies: A New Proof

Holá, L’. (1997)

Serdica Mathematical Journal

Let (X, d) be a metric space and CL(X) the family of all nonempty closed subsets of X. We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric d forces X to be a compact space. In the literature only a more involved and indirect proof using the proximal topology is known. Here we do not need this intermediate step. Moreover we prove that (X, d) is boundedly compact if and only if the bounded Vietoris and Wijsman topologies on CL(X) coincide....

Coloring Cantor sets and resolvability of pseudocompact spaces

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (2018)

Commentationes Mathematicae Universitatis Carolinae

Let us denote by Φ ( λ , μ ) the statement that 𝔹 ( λ ) = D ( λ ) ω , i.e. the Baire space of weight λ , has a coloring with μ colors such that every homeomorphic copy of the Cantor set ℂ in 𝔹 ( λ ) picks up all the μ colors. We call a space X π -regular if it is Hausdorff and for every nonempty open set U in X there is a nonempty open set V such that V ¯ ⊂ U . We recall that a space X is called feebly compact if...

Common Fixed Point Theorems in a Complete 2-metric Space

Debashis Dey, Mantu Saha (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the present paper, we establish a common fixed point theorem for four self-mappings of a complete 2-metric space using the weak commutativity condition and A -contraction type condition and then extend the theorem for a class of mappings.

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