Displaying similar documents to “A remark on R. G. Woods' paper 'The minimum uniform compactification of a metric space' (Fund. Math. 147 (1995), 39–59)”

Extending Peano derivatives: necessary and sufficient conditions

Hans Volkmer (1999)

Fundamenta Mathematicae

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The paper treats functions which are defined on closed subsets of [0,1] and which are k times Peano differentiable. A necessary and sufficient condition is given for the existence of a k times Peano differentiable extension of such a function to [0,1]. Several applications of the result are presented. In particular, functions defined on symmetric perfect sets are studied.

Extending real-valued functions in βκ

Alan Dow (1997)

Fundamenta Mathematicae

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An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality c and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.

Selections that characterize topological completeness

Jan van Mill, Jan Pelant, Roman Pol (1996)

Fundamenta Mathematicae

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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].

Combinatorics of open covers (III): games, Cp (X)

Marion Scheepers (1997)

Fundamenta Mathematicae

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Some of the covering properties of spaces as defined in Parts I and II are here characterized by games. These results, applied to function spaces C p ( X ) of countable tightness, give new characterizations of countable fan tightness and countable strong fan tightness. In particular, each of these properties is characterized by a Ramseyan theorem.