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Fractals of generalized F− Hutchinson operator

Talat Nazir, Sergei Silvestrov, Mujahid Abbas (2016)

Waves, Wavelets and Fractals

The aim of this paper is to construct a fractal with the help of a finite family of F− contraction mappings, a class of mappings more general than contraction mappings, defined on a complete metric space. Consequently, we obtain a variety of results for iterated function systems satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

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...

Free non-archimedean topological groups

Michael Megrelishvili, Menachem Shlossberg (2013)

Commentationes Mathematicae Universitatis Carolinae

We study free topological groups defined over uniform spaces in some subclasses of the class 𝐍𝐀 of non-archimedean groups. Our descriptions of the corresponding topologies show that for metrizable uniformities the corresponding free balanced, free abelian and free Boolean 𝐍𝐀 groups are also metrizable. Graev type ultra-metrics determine the corresponding free topologies. Such results are in a striking contrast with free balanced and free abelian topological groups cases (in standard varieties). Another...

Functional characterizations of p-spaces

Ľubica Holá (2013)

Open Mathematics

We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.

Functor of extension of Λ -isometric maps between central subsets of the unbounded Urysohn universal space

Piotr Niemiec (2010)

Commentationes Mathematicae Universitatis Carolinae

The aim of the paper is to prove that in the unbounded Urysohn universal space 𝕌 there is a functor of extension of Λ -isometric maps (i.e. dilations) between central subsets of 𝕌 to Λ -isometric maps acting on the whole space. Special properties of the functor are established. It is also shown that the multiplicative group ℝ ∖ { 0 } acts continuously on 𝕌 by Λ -isometries.

Further characterizations of boundedly UC spaces

Ľubica Holá, Dušan Holý (1993)

Commentationes Mathematicae Universitatis Carolinae

Following the paper [BDC1], further relations between the classical topologies on function spaces and new ones induced by hyperspace topologies on graphs of functions are introduced and further characterizations of boundedly UC spaces are given.

Further properties of 1-sequence-covering maps

Tran Van An, Luong Quoc Tuyen (2008)

Commentationes Mathematicae Universitatis Carolinae

Some relationships between 1 -sequence-covering maps and weak-open maps or sequence-covering s -maps are discussed. These results are used to generalize a result from Lin S., Yan P., Sequence-covering maps of metric spaces, Topology Appl. 109 (2001), 301–314.

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.

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