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Approximate inverse systems of uniform spaces and an application of inverse systems

Michael G. Charalambous (1991)

Commentationes Mathematicae Universitatis Carolinae

The fundamental properties of approximate inverse systems of uniform spaces are established. The limit space of an approximate inverse sequence of complete metric spaces is the limit of an inverse sequence of some of these spaces. This has an application to the dimension of the limit space of an approximate inverse system. A topologically complete space with dim ≤ n is the limit of an approximate inverse system of metric polyhedra of dim ≤ n . A completely metrizable separable space with dim ≤ n is the limit of an...

Approximate quantities, hyperspaces and metric completeness

Valentín Gregori, Salvador Romaguera (2000)

Bollettino dell'Unione Matematica Italiana

Mostriamo che se X , d è uno spazio metrico completo, allora è completa anche la metrica D , indotta in modo naturale da d sul sottospazio degli insiemi sfocati («fuzzy») di X dati dalle quantità approssimate. Come è ben noto, D è una metrica molto interessante nella teoria dei punti fissi di applicazioni sfocate, poiché permette di ottenere risultati soddisfacenti in questo contesto.

Atomicity of mappings.

Charatonik, Janusz J., Charatonik, Włodzimierz J. (1998)

International Journal of Mathematics and Mathematical Sciences

Aull-paracompactness and strong star-normality of subspaces in topological spaces

Kaori Yamazaki (2004)

Commentationes Mathematicae Universitatis Carolinae

We prove for a subspace Y of a T 1 -space X , Y is (strictly) Aull-paracompact in X and Y is Hausdorff in X if and only if Y is strongly star-normal in X . This result provides affirmative answers to questions of A.V. Arhangel’skii–I.Ju. Gordienko [3] and of A.V. Arhangel’skii [2].

Bi-Lipschitz embeddings of hyperspaces of compact sets

Jeremy T. Tyson (2005)

Fundamenta Mathematicae

We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in ℝ n + 1 ; in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. By way of contrast, the hyperspace K([0,1]) of the...

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