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Universal spaces in the theory of transfinite dimension, II

Wojciech Olszewski (1994)

Fundamenta Mathematicae

We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension ω 0 , or, equivalently, of small transfinite dimension ω 0 ; that is, the family consists of compact metrizable spaces whose transfinite dimension is ω 0 , and every compact metrizable space with transfinite dimension ω 0 is embeddable in a space of the family. We show that the least possible cardinality of such a universal family is equal to the least possible...

Warped compact foliations

Szymon M. Walczak (2008)

Annales Polonici Mathematici

The notion of the Hausdorffized leaf space ˜ of a foliation is introduced. A sufficient condition for warped compact foliations to converge to ˜ is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to ˜ is shown. Finally, some examples are examined.

Weak extent in normal spaces

Ronnie Levy, Mikhail Matveev (2005)

Commentationes Mathematicae Universitatis Carolinae

If X is a space, then the weak extent we ( X ) of X is the cardinal min { α : If 𝒰 is an open cover of X , then there exists A X such that | A | = α and St ( A , 𝒰 ) = X } . In this note, we show that if X is a normal space such that | X | = 𝔠 and we ( X ) = ω , then X does not have a closed discrete subset of cardinality 𝔠 . We show that this result cannot be strengthened in ZFC to get that the extent of X is smaller than 𝔠 , even if the condition that we ( X ) = ω is replaced by the stronger condition that X is separable.

Weakly fuzzy topological entropy

B M Uzzal Afsan (2022)

Mathematica Bohemica

In 2005, İ. Tok fuzzified the notion of the topological entropy R. A. Adler et al. (1965) using the notion of fuzzy compactness of C. L. Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R. A. Adler et al. (1965) of continuous mapping...

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