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A characterization of tribes with respect to the Łukasiewicz t -norm

Erich Peter Klement, Mirko Navara (1997)

Czechoslovak Mathematical Journal

We give a complete characterization of tribes with respect to the Łukasiewicz t -norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz t -norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental t -norms, e. g., for the product t -norm.

A new approach for KM-fuzzy partial metric spaces

Yu Shen, Chong Shen, Conghua Yan (2022)

Kybernetika

The main purpose of this paper is to give a new approach for partial metric spaces. We first provide the new concept of KM-fuzzy partial metric, as an extension of both the partial metric and KM-fuzzy metric. Then its relationship with the KM-fuzzy quasi-metric is established. In particularly, we construct a KM-fuzzy quasi-metric from a KM-fuzzy partial metric. Finally, after defining the notion of partial pseudo-metric systems, a one-to-one correspondence between partial pseudo-metric systems and...

A non-archimedean Dugundji extension theorem

Jerzy Kąkol, Albert Kubzdela, Wiesƚaw Śliwa (2013)

Czechoslovak Mathematical Journal

We prove a non-archimedean Dugundji extension theorem for the spaces C * ( X , 𝕂 ) of continuous bounded functions on an ultranormal space X with values in a non-archimedean non-trivially valued complete field 𝕂 . Assuming that 𝕂 is discretely valued and Y is a closed subspace of X we show that there exists an isometric linear extender T : C * ( Y , 𝕂 ) → C * ( X , 𝕂 ) if X is collectionwise normal or Y is Lindelöf or 𝕂 is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace Y of an ultraregular...

Almost periodic sequences and functions with given values

Michal Veselý (2011)

Archivum Mathematicum

We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set  X in a metric space, it is proved the existence of an almost periodic sequence { ψ k } k ∈ ℤ such that { ψ k ; k ∈ ℤ } = X and ψ k = ψ k + l q ( k ) , l ∈ ℤ for all  k and some q ( k ) ∈ ℕ which depends on  k .

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