Vietoris topology on spaces dominated by second countable ones
Copyright policy )Vietoris topology on spaces dominated by second countable ones
Abstract For a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = {FK : K ∈ C(M)} ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂ FL for any K;L ∈ C(M). A space X is strongly dominated by a space M if there exists an M-ordered compact cover F such that for any compact K ⊂ X there is F ∈ F such that K ⊂ F . Let K(X) D C(X)\{Ø} be the set of all nonempty compact subsets of a space X endowed with the Vietoris topology. We prove that a space X is strongly dominated by a space M if and only if K(X) is strongly dominated by M and an example is given of a σ-compact space X such that K(X) is not Lindelöf†. It is stablished that if the weight of a scattered compact space X is not less than c, then the spaces Cp(K(X)) and K(Cp(X)) are not Lindelöf Σ. We show that if X is the one-point compactification of a discrete space, then the hyperspace K(X) is semi-Eberlein compact.
Study of properties and structures of commutative rings, Topological Vector Spaces, Special maps on topological spaces (open, closed, perfect, etc.), Vietoris topology, scattered spaces, FOS: Mechanical engineering, Separable space, Relatively compact subspace, Engineering, lindelöf -space, Real-valued functions in general topology, Second-countable space, Hyperspaces in general topology, one-point compactification, Compactification (mathematics), Mathematical Physics, Model Theory and Topological Dynamics, Local compactness, \(\sigma\)-compactness, Eberlein compact, Discrete mathematics, Mechanical engineering, FOS: Philosophy, ethics and religion, Topological vector space, Lindelöf-space, Physical Sciences, Isolated point, strong domination by second countable spaces, Theory of Banach Spaces and Operators, Polish space, Noncompact covering properties (paracompact, Lindelöf, etc.), Lindelöf p-space, Regular space, Compact space, Space (punctuation), Mathematical analysis, eberlein compact, Function spaces in general topology, QA1-939, FOS: Mathematics, Scattered spaces, Cover (algebra), Topology (electrical circuits), Algebra and Number Theory, Countable set, Hyperspace, Pure mathematics, lindelöf p-space, hemicompact space, Linguistics, Locally compact space, Philosophy, Combinatorics, FOS: Languages and literature, vietoris topology, Geometry and Topology, Mathematics, Topological space
Study of properties and structures of commutative rings, Topological Vector Spaces, Special maps on topological spaces (open, closed, perfect, etc.), Vietoris topology, scattered spaces, FOS: Mechanical engineering, Separable space, Relatively compact subspace, Engineering, lindelöf -space, Real-valued functions in general topology, Second-countable space, Hyperspaces in general topology, one-point compactification, Compactification (mathematics), Mathematical Physics, Model Theory and Topological Dynamics, Local compactness, \(\sigma\)-compactness, Eberlein compact, Discrete mathematics, Mechanical engineering, FOS: Philosophy, ethics and religion, Topological vector space, Lindelöf-space, Physical Sciences, Isolated point, strong domination by second countable spaces, Theory of Banach Spaces and Operators, Polish space, Noncompact covering properties (paracompact, Lindelöf, etc.), Lindelöf p-space, Regular space, Compact space, Space (punctuation), Mathematical analysis, eberlein compact, Function spaces in general topology, QA1-939, FOS: Mathematics, Scattered spaces, Cover (algebra), Topology (electrical circuits), Algebra and Number Theory, Countable set, Hyperspace, Pure mathematics, lindelöf p-space, hemicompact space, Linguistics, Locally compact space, Philosophy, Combinatorics, FOS: Languages and literature, vietoris topology, Geometry and Topology, Mathematics, Topological space
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