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Displaying 1061 – 1080 of 1531

On the complexity of some $σ$ -ideals of $σ$ -P-porous sets

Luděk Zajíček, Miroslav Zelený (2003)

Commentationes Mathematicae Universitatis Carolinae

Let $𝐏$ be a porosity-like relation on a separable locally compact metric space $E$ . We show that the $σ$ -ideal of compact $σ$ - $𝐏$ -porous subsets of $E$ (under some general conditions on $𝐏$ and $E$ ) forms a $Π_{1}^{1}$ -complete set in the hyperspace of all compact subsets of $E$ , in particular it is coanalytic and non-Borel. Our general results are applicable to most interesting types of porosity. It is shown in the cases of the $σ$ -ideals of $σ$ -porous sets, $σ$ - $〈 g 〉$ -porous sets, $σ$ -strongly porous sets, $σ$ -symmetrically porous sets...

On the complexity of subspaces of $S_{ω}$

Carlos Uzcátegui (2003)

Fundamenta Mathematicae

Let (X,τ) be a countable topological space. We say that τ is an analytic (resp. Borel) topology if τ as a subset of the Cantor set $2^{X}$ (via characteristic functions) is an analytic (resp. Borel) set. For example, the topology of the Arkhangel’skiĭ-Franklin space $S_{ω}$ is $F_{σ δ}$ . In this paper we study the complexity, in the sense of the Borel hierarchy, of subspaces of $S_{ω}$ . We show that $S_{ω}$ has subspaces with topologies of arbitrarily high Borel rank and it also has subspaces with a non-Borel topology. Moreover,...

On the concept of E-regularity for fuzzy topology

A. Šostak (1989)

Matematički Vesnik

On the concepts of balls in a $D$ -metric space.

Naidu, S.V.R., Rao, K.P.R., Srinivasa Rao, N. (2005)

International Journal of Mathematics and Mathematical Sciences

On the connectedness of boundary and complement for domains

Andrzej Czarnecki, Marcin Kulczycki, Wojciech Lubawski (2011)

Annales Polonici Mathematici

This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in ℝⁿ is equivalent to the connectedness of its complement.

On the connectedness of some topological spaces

Giuseppe Paxia, Irene Sergio (1989)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

On the connected-open topology

Gauld, D.B. (1977)

Portugaliae mathematica

On the Connes operator in Hochschild homology.

Ndombol, Bitjong (2005)

AMA. Algebra Montpellier Announcements [electronic only]

On the construction of biconnected sets

V. Neumann-Lara, R. G. Wilson (1986)

Matematički Vesnik

On the construction of the extensional topological hull

I. W. Alderton, F. Schwartz, S. Weck-Schwarz (1994)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

On the continua which are Cantor homogeneous or arcwise homogeneous

K. Omiljanowski, H. Patkowska (1990)

Colloquium Mathematicae

On the continuity and monotonicity of restrictions of connected functions

Ryszard Pawlak (1981)

Fundamenta Mathematicae

On the continuity of functions.

Almeida, Ricardo (2007)

APPS. Applied Sciences

On the Continuity of Internal Functions

Hermann Render (1993)

Publications de l'Institut Mathématique

On the continuity of midpoint hall convex set-valued functions.

Antonella Fiacca, Francesca Papalini (1994)

Aequationes mathematicae

On the continuity of midpoint hull convex set-valued functions. (Summary).

Antonella Fiacca, Francesca Papalini (1994)

Aequationes mathematicae

On the continuity of the elements of the Ellis semigroup and other properties

Salvador García-Ferreira, Yackelin Rodríguez-López, Carlos Uzcátegui (2021)

Commentationes Mathematicae Universitatis Carolinae

We consider discrete dynamical systems whose phase spaces are compact metrizable countable spaces. In the first part of the article, we study some properties that guarantee the continuity of all functions of the corresponding Ellis semigroup. For instance, if every accumulation point of $X$ is fixed, we give a necessary and sufficient condition on a point $a \in X^{'}$ in order that all functions of the Ellis semigroup $E (X, f)$ be continuous at the given point $a$ . In the second part, we consider transitive dynamical...

On the continuity of the pressure for monotonic mod one transformations

Peter Raith (2000)

Commentationes Mathematicae Universitatis Carolinae

If $f : [0, 1] \to ℝ$ is strictly increasing and continuous define $T_{f} x = f (x) (mod 1)$ . A transformation $\tilde{T} : [0, 1] \to [0, 1]$ is called $ε$ -close to $T_{f}$ , if $\tilde{T} x = \tilde{f} (x) (mod 1)$ for a strictly increasing and continuous function $\tilde{f} : [0, 1] \to ℝ$ with $∥ \tilde{f} {- f ∥}_{\infty} < ε$ . It is proved that the topological pressure $p (T_{f}, g)$ is lower semi-continuous, and an upper bound for the jumps up is given. Furthermore the continuity of the maximal measure is shown, if a certain condition is satisfied. Then it is proved that the topological pressure is upper semi-continuous for every continuous function $g : [0, 1] \to ℝ$ , if and only if $0$ is...

On the convergence and character spectra of compact spaces

István Juhász, William A. R. Weiss (2010)

Fundamenta Mathematicae

An infinite set A in a space X converges to a point p (denoted by A → p) if for every neighbourhood U of p we have |A∖U| < |A|. We call cS(p,X) = |A|: A ⊂ X and A → p the convergence spectrum of p in X and cS(X) = ⋃cS(x,X): x ∈ X the convergence spectrum of X. The character spectrum of a point p ∈ X is χS(p,X) = χ(p,Y): p is non-isolated in Y ⊂ X, and χS(X) = ⋃χS(x,X): x ∈ X is the character spectrum of X. If κ ∈ χS(p,X) for a compactum X then κ,cf(κ) ⊂ cS(p,X). A selection of our results (X...

On the convergence of certain sequences and some applications

M. R. Tasković (1977)

Matematički Vesnik

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