EuDML | Browse

In the present paper conditions are studied, under which a pseudo-orbit of a continuous map $f : M \to M$ , where $M$ is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map $f$ .

On a weak form of uniform convergence

Jaroslav Fuka, Petr Holický (2005)

Commentationes Mathematicae Universitatis Carolinae

The notion of $Δ$ -convergence of a sequence of functions is stronger than pointwise convergence and weaker than uniform convergence. It is inspired by the investigation of ill-posed problems done by A.N. Tichonov. We answer a question posed by M. Katětov around 1970 by showing that the only analytic metric spaces $X$ for which pointwise convergence of a sequence of continuous real valued functions to a (continuous) limit function on $X$ implies $Δ$ -convergence are $σ$ -compact spaces. We show that the assumption...

On Asymmetric Distances

Andrea C.G. Mennucci (2013)

Analysis and Geometry in Metric Spaces

In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the...

On butterfly-points in $β X$ , Tychonoff products and weak Lindelöf numbers

Sergei Logunov (2022)

Commentationes Mathematicae Universitatis Carolinae

Let $X$ be the Tychonoff product $\prod_{α < τ} X_{α}$ of $τ$ -many Tychonoff non-single point spaces $X_{α}$ . Let $p \in X^{*}$ be a point in the closure of some $G \subset X$ whose weak Lindelöf number is strictly less than the cofinality of $τ$ . Then we show that $β X ∖ {p}$ is not normal. Under some additional assumptions, $p$ is a butterfly-point in $β X$ . In particular, this is true if either $X = ω^{τ}$ or $X = R^{τ}$ and $τ$ is infinite and not countably cofinal.

On certain homological properties of finite-dimensional compacta. Carriers, minimal carriers and bubbles

W. Kuperberg (1973)

Fundamenta Mathematicae

On certain properties characterizing locally separable metric spaces

Tibor Neubrunn, Jaroslav Smítal, Tibor Šalát (1967)

Časopis pro pěstování matematiky

On certain types of convergences

Ján Borsík (1992)

Mathematica Bohemica

Mappings preserving Cauchy sequences and certain types of convergences connected with these mappings are investigated.

On character of points in the Higson corona of a metric space

Taras O. Banakh, Ostap Chervak, Lubomyr Zdomskyy (2013)

Commentationes Mathematicae Universitatis Carolinae

We prove that for an unbounded metric space $X$ , the minimal character $𝗆 χ (\overset{ˇ}{X})$ of a point of the Higson corona $\overset{ˇ}{X}$ of $X$ is equal to $𝔲$ if $X$ has asymptotically isolated balls and to $max {𝔲, 𝔡}$ otherwise. This implies that under $𝔲 < 𝔡$ a metric space $X$ of bounded geometry is coarsely equivalent to the Cantor macro-cube $2^{< ℕ}$ if and only if $dim (\overset{ˇ}{X}) = 0$ and $𝗆 χ (\overset{ˇ}{X}) = 𝔡$ . This contrasts with a result of Protasov saying that under CH the coronas of any two asymptotically zero-dimensional unbounded metric separable spaces are homeomorphic.

Currently displaying 1 – 20 of 103

Page 1 Next

Displaying 1 – 20 of 103

O množinách vzdialeností množín metrického priestoru

On a certain lattice of topologies on a product of metric spaces

On a class of topological spaces with a Scott sentence

On a functional inequality arising in the construction of the product of several metric spaces.

On a metrization of the hyperspace of a metric space

On a problem of J. Nagata

On a problem of Sikorski

On a product of metric spaces

On a property of pseudometrics and uniformities near to convexity

On a shadowing lemma in metric spaces

On a weak form of uniform convergence

On Asymmetric Distances

On butterfly-points in $β X$ , Tychonoff products and weak Lindelöf numbers

On certain homological properties of finite-dimensional compacta. Carriers, minimal carriers and bubbles

On certain properties characterizing locally separable metric spaces

On certain types of convergences

On character of points in the Higson corona of a metric space

On Ciric's fixed point theorem

On cliquish functions on product spaces

On closed and inductively closed images of products of metric spaces

Currently displaying 1 – 20 of 103