Displaying similar documents to “A function space from a compact metrizable space to a dendrite with the hypo-graph topology”

A Hilbert cube compactification of the function space with the compact-open topology

Atsushi Kogasaka, Katsuro Sakai (2009)

Open Mathematics

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Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification C ¯ (X) of C(X) such that the pair ( C ¯ (X), C(X)) is homeomorphic to (Q,...

Spaces of ω-limit sets of graph maps

Jie-Hua Mai, Song Shao (2007)

Fundamenta Mathematicae

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Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.

Some news about the independence number of a graph

Jochen Harant (2000)

Discussiones Mathematicae Graph Theory

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For a finite undirected graph G on n vertices some continuous optimization problems taken over the n-dimensional cube are presented and it is proved that their optimum values equal the independence number of G.