AbstractWe construct a separable metric space E in R3 for which both the small and large compactness degrees cmpE=CmpE=1 and the compactness deficiency defE=2. This improves on the example in R4 given by R. Pol (1992) as a counterexample to the well-known conjecture of J. de Groot
AbstractA compactification αX of a space X is a C-compactification if αX is a C-space. In this paper...
Throughout C(X) will denote the ring of all continuous real-valued functions on a Tychonoff space X,...
AbstractWe show in ZF that:(i)A countably compact metric space need not be limit point compact or to...
AbstractWe construct a separable metric space E in R3 for which both the small and large compactness...
AbstractRecently, De Groot's conjecture that cmp X = def X holds for every separable and metrizable ...
AbstractFor each pair of positive integers k and m with k⩽m there exists a separable metrizable spac...
AbstractIt is known that the Stone–Čech compactification βX of a noncompact metrizable space X is ap...
summary:We answer a question of I. Juhasz by showing that MA $+ \neg$ CH does not imply that every c...
summary:We answer a question of I. Juhasz by showing that MA $+ \neg$ CH does not imply that every c...
AbstractIn [J.M. Aarts, T. Nishiura, Dimension and Extensions, North-Holland, Amsterdam, 1993], Aart...
A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with ...
summary:We construct a space having the properties in the title, and with the same technique, a coun...
AbstractOur main result is that the following cardinal arithmetic assumption, which is a slight weak...
summary:We construct a space having the properties in the title, and with the same technique, a coun...
Throughout C(X) will denote the ring of all continuous real-valued functions on a Tychonoff space X,...
AbstractA compactification αX of a space X is a C-compactification if αX is a C-space. In this paper...
Throughout C(X) will denote the ring of all continuous real-valued functions on a Tychonoff space X,...
AbstractWe show in ZF that:(i)A countably compact metric space need not be limit point compact or to...
AbstractWe construct a separable metric space E in R3 for which both the small and large compactness...
AbstractRecently, De Groot's conjecture that cmp X = def X holds for every separable and metrizable ...
AbstractFor each pair of positive integers k and m with k⩽m there exists a separable metrizable spac...
AbstractIt is known that the Stone–Čech compactification βX of a noncompact metrizable space X is ap...
summary:We answer a question of I. Juhasz by showing that MA $+ \neg$ CH does not imply that every c...
summary:We answer a question of I. Juhasz by showing that MA $+ \neg$ CH does not imply that every c...
AbstractIn [J.M. Aarts, T. Nishiura, Dimension and Extensions, North-Holland, Amsterdam, 1993], Aart...
A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with ...
summary:We construct a space having the properties in the title, and with the same technique, a coun...
AbstractOur main result is that the following cardinal arithmetic assumption, which is a slight weak...
summary:We construct a space having the properties in the title, and with the same technique, a coun...
Throughout C(X) will denote the ring of all continuous real-valued functions on a Tychonoff space X,...
AbstractA compactification αX of a space X is a C-compactification if αX is a C-space. In this paper...
Throughout C(X) will denote the ring of all continuous real-valued functions on a Tychonoff space X,...
AbstractWe show in ZF that:(i)A countably compact metric space need not be limit point compact or to...
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