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1
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C(K) spaces which cannot be uniformly embedded into c₀(Γ)

100%
Pelant J., Holický P., Kalenda O.
Fundamenta Mathematicae
|
2006
|
tom 192
|
nr 3
245-254
EN
We give two examples of scattered compact spaces K such that C(K) is not uniformly homeomorphic to any subset of c₀(Γ) for any set Γ. The first one is [0,ω₁] and hence it has the smallest possible cardinality, the other one has the smallest possible height ω₀ + 1.
2
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Selections that characterize topological completeness

100%
van Mill J., Pelant J., Pol R.
Fundamenta Mathematicae
|
1996
|
tom 149
|
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].
3
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The space of ultrafilters on N covered by nowhere dense sets

100%
Balcar B., Pelant J., Simon P.
Fundamenta Mathematicae
|
1980
|
tom 110
|
nr 1
11-24
4
Content available remote

Selections and suborderability

88%
Artico G., Marconi U., Pelant J., Rotter L., Tkachenko M.
Fundamenta Mathematicae
|
2002
|
tom 175
|
nr 1
1-33
EN
We extend van Mill-Wattel's results and show that each countably compact completely regular space with a continuous selection on couples is suborderable. The result extends also to pseudocompact spaces if they are either scattered, first countable, or connected. An infinite pseudocompact topological group with such a continuous selection is homeomorphic to the Cantor set. A zero-selection is a selection on the hyperspace of closed sets which chooses always an isolated point of a set. Extending Fujii-Nogura results, we show that an almost compact space with a continuous zero-selection is homeomorphic to some ordinal space, and a (locally compact) pseudocompact space with a continuous zero-selection is an (open) subspace of some space of ordinals. Under the Diamond Principle, we construct several counterexamples, e.g. a locally compact locally countable monotonically normal space with a continuous zero-selection which is not suborderable.
5
Content available remote

The smallest number of free closed filters

87%
Pelant J., Simon P., Vaughan J. E.
Fundamenta Mathematicae
|
1988
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tom 131
|
nr 3
215-221
6
Content available remote

On supercomplete uniform spaces IV: Countable products

74%
Hohti A., Pelant J.
Fundamenta Mathematicae
|
1990
|
tom 136
|
nr 2
115-120
7
Content available remote

On complexity of metric spaces

62%
Hohti A., Pelant J.
Fundamenta Mathematicae
|
1985
|
tom 125
|
nr 2
133-142
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