Displaying similar documents to “Remark on some abstract distance spaces.”

Isomorphically isometric probabilistic normed linear spaces.

Howard Sherwood (1979)

Stochastica

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Probabilistic normed linear spaces (briefly PNL spaces) were first studied by A. N. Serstnev in [1]. His definition was motivated by the definition of probabilistic metric spaces (PM spaces) which were introduced by K. Menger and subsequebtly developed by A. Wald, B. Schweizer, A. Sklar and others. In a previuos paper [2] we studied the relationship between two important classes of PM spaces, namely E-spaces and pseudo-metrically generated PM spaces. We showed that a PM space...

Factorwise rigidity of embeddings of products of pseudo-arcs

Mauricio E. Chacón-Tirado, Alejandro Illanes, Rocío Leonel (2012)

Colloquium Mathematicae

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An embedding from a Cartesian product of two spaces into the Cartesian product of two spaces is said to be factorwise rigid provided that it is the product of embeddings on the individual factors composed with a permutation of the coordinates. We prove that each embedding of a product of two pseudo-arcs into itself is factorwise rigid. As a consequence, if X and Y are metric continua with the property that each of their nondegenerate proper subcontinua is homeomorphic to the pseudo-arc,...