Uniformizable Cauchy spaces.
We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension , or, equivalently, of small transfinite dimension ; that is, the family consists of compact metrizable spaces whose transfinite dimension is , and every compact metrizable space with transfinite dimension 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...
In this paper the concept of a fuzzy contraction mapping on a fuzzy metric space is introduced and it is proved that every fuzzy contraction mapping on a complete fuzzy metric space has a unique fixed point.
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.
If is a space, then the weak extent of is the cardinal If is an open cover of , then there exists such that and . In this note, we show that if is a normal space such that and , then does not have a closed discrete subset of cardinality . We show that this result cannot be strengthened in ZFC to get that the extent of is smaller than , even if the condition that is replaced by the stronger condition that is separable.
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...