Classification of function spaces with the pointwise topology determined by a countable dense set
Tadeusz Dobrowolski, Witold Marciszewski (1995)
Fundamenta Mathematicae
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Tadeusz Dobrowolski, Witold Marciszewski (1995)
Fundamenta Mathematicae
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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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his.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.
Sy Friedman (1997)
Fundamenta Mathematicae
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We present a reformulation of the fine structure theory from Jensen [72] based on his Σ* theory for K and introduce the Fine Structure Principle, which captures its essential content. We use this theory to prove the Square and Fine Scale Principles, and to construct Morasses.
Taka-Aki Tanaka (1996)
Acta Arithmetica
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Stanisław Świerczkowski (1995)
Fundamenta Mathematicae
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Hans Peter Schlickewei, Wolfgang M. Schmidt (1995)
Acta Arithmetica
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Yoshiharu Kohayakawa, Tomasz Łuczak, Vojtěch Rödl (1996)
Acta Arithmetica
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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 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.