Displaying similar documents to “The omega limit sets of subsets in a metric space”

Gradient systems of closed operators

Vittorino Pata (2009)

Open Mathematics

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A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.

On character of points in the Higson corona of a metric space

Taras O. Banakh, Ostap Chervak, Lubomyr Zdomskyy (2013)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for an unbounded metric space X , the minimal character 𝗆 χ ( X ˇ ) of a point of the Higson corona X ˇ of X is equal to 𝔲 if X has asymptotically isolated balls and to max { 𝔲 , 𝔡 } otherwise. This implies that under 𝔲 < 𝔡 a metric space X of bounded geometry is coarsely equivalent to the Cantor macro-cube 2 < ℕ if and only if dim ( X ˇ ) = 0 and 𝗆 χ ( X ˇ ) = 𝔡 . This contrasts with a result of Protasov saying that under CH the coronas of any two asymptotically zero-dimensional unbounded metric separable spaces are homeomorphic. ...

On unrestricted products of (W) contractions

W. Bartoszek (2000)

Colloquium Mathematicae

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Given a family of (W) contractions T 1 , . . . , T N on a reflexive Banach space X we discuss unrestricted sequences T r n ∘ . . . ∘ T r 1 ( x ) . We show that they converge weakly to a common fixed point, which depends only on x and not on the order of the operators T r n if and only if the weak operator closed semigroups generated by T 1 , . . . , T N are right amenable.

Strong pseudocompact properties

Salvador García-Ferreira, Y. F. Ortiz-Castillo (2014)

Commentationes Mathematicae Universitatis Carolinae

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For a free ultrafilter p on ℕ , the concepts of strong pseudocompactness, strong p -pseudocompactness and pseudo- ω -boundedness were introduced in [Angoa J., Ortiz-Castillo Y.F., Tamariz-Mascarúa A., Ultrafilters and properties related to compactness, Topology Proc. 43 (2014), 183–200] and [García-Ferreira S., Ortiz-Castillo Y.F., Strong pseudocompact properties of certain subspaces of ℕ * , submitted]. These properties in a space X characterize the pseudocompactness of the hyperspace 𝒦 ( X ) of compact...