Displaying similar documents to “The Σ* approach to the fine structure of L”

Does C* -embedding imply C*-embedding in the realm of products with a non-discrete metric factor?

Valentin Gutev, Haruto Ohta (2000)

Fundamenta Mathematicae

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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.

Countable Toronto spaces

Gary Gruenhage, J. Moore (2000)

Fundamenta Mathematicae

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A space X is called an α-Toronto space if X is scattered of Cantor-Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each α < ω 1 .

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.