DML-PL - Yadda

1

Selections that characterize topological completeness

100%

van Mill J., Pelant J., Pol R.

Fundamenta Mathematicae

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1996

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tom 149

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nr 2

127-141

EN

We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].

2

Vietoris topology on spaces dominated by second countable ones

63%

Islas C., Jardon D.

Open Mathematics

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2015

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tom 13

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nr 1

EN

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.

3

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Decomposition of topologies on lattices and hyperspaces

46%

Costantini C., Vitolo P.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction.................................................................................5 1. Decomposable topologies.......................................................6 2. Locally convex topologies......................................................10 3. Semilattices. Strong decomposability.....................................13 4. Convex topologies.................................................................15 5. Topologies on linearly ordered sets.......................................18 6. Topologies on lattices............................................................20 7. The Scott topology.................................................................26 8. Uniqueness of decomposition................................................28 9. Hyperspace topologies..........................................................32 10. The Vietoris topology...........................................................35 11. The Hausdorff metric topology.............................................37 12. The proximal topology..........................................................39 13. The Kuratowski convergence..............................................40 14. Uniqueness of decomposition for hypertopologies..............44 References................................................................................47

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Open Mathematics

1 Costantini C.

1 Islas C.

1 Jardon D.

1 Pelant J.

1 Pol R.

1 Vitolo P.

1 van Mill J.

1 2015

1 1999

1 1996

Wyniki wyszukiwania

Selections that characterize topological completeness

Vietoris topology on spaces dominated by second countable ones

Decomposition of topologies on lattices and hyperspaces