The omega limit sets of subsets in a metric space

Changming Ding

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 $𝗆 χ (\overset{ˇ}{X})$ of a point of the Higson corona $\overset{ˇ}{X}$ 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 $dim (\overset{ˇ}{X}) = 0$ and $𝗆 χ (\overset{ˇ}{X}) = 𝔡$ . 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 $T_{r_{n}} \circ . . . \circ T_{r_{1}} (x)$ . 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.

On Conley's fundamental theorem of dynamical systems.

Razvan, M.R. (2004)

International Journal of Mathematics and Mathematical Sciences

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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...

On completeness of quasi-pseudometric spaces.

Moshokoa, Seithuti P. (2005)

International Journal of Mathematics and Mathematical Sciences

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