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In his paper "Continuous mappings on continua" [5], T. Maćkowiak collected results concerning mappings on metric continua. These results are theorems, counterexamples, and unsolved problems and are listed in a series of tables at the ends of chapters. It is the purpose of the present paper to provide solutions (three proofs and one example) to four of those problems.

Fragmentability and compactness in C(K)-spaces

B. Cascales, G. Manjabacas, G. Vera (1998)

Studia Mathematica

Let K be a compact Hausdorff space, $C_{p} (K)$ the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and $t_{p} (D)$ the topology in C(K) of pointwise convergence on D. It is proved that when $C_{p} (K)$ is Lindelöf the $t_{p} (D)$ -compact subsets of C(K) are fragmented by the supremum norm of C(K). As a consequence we obtain some Namioka type results and apply them to prove that if K is separable and $C_{p} (K)$ is Lindelöf, then K is metrizable if, and only if, there is a countable and dense...

Fuzziness and fuzzy equality

Aleš Pultr (1982)

Commentationes Mathematicae Universitatis Carolinae

Fuzzy distances

Josef Bednář (2005)

Kybernetika

In the paper, three different ways of constructing distances between vaguely described objects are shown: a generalization of the classic distance between subsets of a metric space, distance between membership functions of fuzzy sets and a fuzzy metric introduced by generalizing a metric space to fuzzy-metric one. Fuzzy metric spaces defined by Zadeh’s extension principle, particularly to $ℝ^{n}$ are dealt with in detail.

Fuzzy metrics and statistical metric spaces

Ivan Kramosil, Jiří Michálek (1975)

Kybernetika

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First order topology [Book]

Foundations of Vietoris homology theory with applications to non-compact spaces [Book]

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