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The problem of continuous simultaneous extension of all continuous partial ultrametrics defined on closed subsets of a compact zero-dimensional metric space was recently solved by E.D. Tymchatyn and M. Zarichnyi and improvements to their result were made by I. Stasyuk. In the current paper we extend these results to complete, bounded, zero-dimensional metric spaces and to both continuous and uniformly continuous partial ultrametrics.

A fixed point principle for locally expansive multifunctions

Solomon Leader (1980)

Fundamenta Mathematicae

A Fixed Point Theorem for a Class of Mappings.

Chi Song Wong (1973)

Mathematische Annalen

A Mapping Theorem on Aleph-spaces

Zhaowen Li (2005)

Matematički Vesnik

A metric on the space of projections admitting nice isometries

Lajos Molnár, Werner Timmermann (2009)

Studia Mathematica

Motivated by the concept of separation between propositions in quantum logic, we introduce the so-called separation metric or Santos metric on the space of all projections in a Hilbert space. We show that the resulting metric space has only "nice" surjective isometries. On the nontrivial projections they are all unitarily or antiunitarily equivalent to the identity or to taking the orthogonal complement. We relate this result to Wigner's classical theorem on the form of quantum mechanical symmetry...

A new characterization of spaces with locally countable $s n$ -networks

Luong Quoc Tuyen (2013)

Matematički Vesnik

A note on operators extending partial ultrametrics

Edward D. Tymchatyn, Michael M. Zarichnyi (2005)

Commentationes Mathematicae Universitatis Carolinae

We consider the question of simultaneous extension of partial ultrametrics, i.e. continuous ultrametrics defined on nonempty closed subsets of a compact zero-dimensional metrizable space. The main result states that there exists a continuous extension operator that preserves the maximum operation. This extension can also be chosen so that it preserves the Assouad dimension.

A note on sequence-covering $π$ -images of metric spaces

Zhaowen Li, Tusheng Xie (2012)

Matematički Vesnik

A note on $ℵ$ -spaces and $g$ -metrizable spaces

Zhaowen Li (2005)

Czechoslovak Mathematical Journal

In this paper, we give the mapping theorems on $ℵ$ -spaces and $g$ -metrizable spaces by means of some sequence-covering mappings, mssc-mappings and $π$ -mappings.

A Theorem On Contraction Mappings

S. A. Husain, V. M. Sehgal (1978)

Publications de l'Institut Mathématique

A theorem on contraction mappings.

S.A. Husain, V.M. Sengal (1978)

Publications de l'Institut Mathématique [Elektronische Ressource]

A theorem on contractive mappings

S. Č. Nešić (1992)

Matematički Vesnik

About $w c s$ -covers and $w c s^{*}$ -networks on the Vietoris hyperspace $ℱ (X)$

Luong Quoc Tuyen, Ong V. Tuyen, Phan D. Tuan, Nguzen X. Truc (2023)

Commentationes Mathematicae Universitatis Carolinae

We study some generalized metric properties on the hyperspace $ℱ (X)$ of finite subsets of a space $X$ endowed with the Vietoris topology. We prove that $X$ has a point-star network consisting of (countable) $w c s$ -covers if and only if so does $ℱ (X)$ . Moreover, $X$ has a sequence of $w c s$ -covers with property $(P)$ which is a point-star network if and only if so does $ℱ (X)$ , where $(P)$ is one of the following properties: point-finite, point-countable, compact-finite, compact-countable, locally finite, locally countable. On the other...

An Exactly Two-to-One Map from an Indecomposable Chainable Continuum

Jerzy Krzempek (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.

An invariant of bi-Lipschitz maps

Hossein Movahedi-Lankarani (1993)

Fundamenta Mathematicae

A new numerical invariant for the category of compact metric spaces and Lipschitz maps is introduced. This invariant takes a value less than or equal to 1 for compact metric spaces that are Lipschitz isomorphic to ultrametric ones. Furthermore, a theorem is provided which makes it possible to compute this invariant for a large class of spaces. In particular, by utilizing this invariant, it is shown that neither a fat Cantor set nor the set $0 \cup {1 / n}_{n \geq 1}$ is Lipschitz isomorphic to an ultrametric space.

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