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Displaying 421 – 440 of 453

Universal metric spaces

Pelant, Jan (1976)

Seminar Uniform Spaces

Upper semicontinuous decompositions of convex metric spaces

Stephen Rodabaugh (1980)

Fundamenta Mathematicae

Valuations of lines

Josef Mlček (1992)

Commentationes Mathematicae Universitatis Carolinae

We enlarge the problem of valuations of triads on so called lines. A line in an $e$ -structure $𝔸 = 〈 A, F, E 〉$ (it means that $〈 A, F 〉$ is a semigroup and $E$ is an automorphism or an antiautomorphism on $〈 A, F 〉$ such that $E \circ E = 𝐈𝐝 ↾ A$ ) is, generally, a sequence $𝔸 ↾ B$ , $𝔸 ↾ U_{c}$ , $c \in 𝐅𝐙$ (where $𝐅𝐙$ is the class of finite integers) of substructures of $𝔸$ such that $B \subseteq U_{c} \subseteq U_{d}$ holds for each $c \leq d$ . We denote this line as $𝔸 {(U_{c}, B)}_{c \in 𝐅𝐙}$ and we say that a mapping $H$ is a valuation of the line $𝔸 {(U_{c}, B)}_{c \in 𝐅𝐙}$ in a line $\hat{𝔸} {({\hat{U}}_{c}, \hat{B})}_{c \in 𝐅𝐙}$ if it is, for each $c \in 𝐅𝐙$ , a valuation of the triad $𝔸 (U_{c}, B)$ in $\hat{𝔸} ({\hat{U}}_{c}, \hat{B})$ . Some theorems on an existence of...

Valuations of structures

Josef Mlček (1979)

Commentationes Mathematicae Universitatis Carolinae

Whitney maps-a non-metric case

Janusz Charatonik, Włodzimierz Charatonik (2000)

Colloquium Mathematicae

It is shown that there is no Whitney map on the hyperspace $2^{X}$ for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).

Zero-dimensional countable dense unions of Z-sets in the Hilbert cube

D. Curtis, Jan van Mill (1983)

Fundamenta Mathematicae

Zone and double zone diagrams in abstract spaces

Daniel Reem, Simeon Reich (2009)

Colloquium Mathematicae

A zone diagram of order n is a relatively new concept which was first defined and studied by T. Asano, J. Matoušek and T. Tokuyama. It can be interpreted as a state of equilibrium between n mutually hostile kingdoms. Formally, it is a fixed point of a certain mapping. These authors considered the Euclidean plane with finitely many singleton-sites and proved the existence and uniqueness of zone diagrams there. In the present paper we generalize this concept in various ways. We consider general sites...

Zur Topologisierung metrischer Räume. I.

R.Z. Domiaty (1973)

Journal für die reine und angewandte Mathematik

$σ$ -porosity is separably determined

Marek Cúth, Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

We prove a separable reduction theorem for $σ$ -porosity of Suslin sets. In particular, if $A$ is a Suslin subset in a Banach space $X$ , then each separable subspace of $X$ can be enlarged to a separable subspace $V$ such that $A$ is $σ$ -porous in $X$ if and only if $A \cap V$ is $σ$ -porous in $V$ . Such a result is proved for several types of $σ$ -porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem...