On the concept of E-regularity for fuzzy topology
On the concepts of balls in a -metric space.
On the connectedness of boundary and complement for domains
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
On the connected-open topology
On the Connes operator in Hochschild homology.
On the construction of biconnected sets
On the construction of the extensional topological hull
On the continua which are Cantor homogeneous or arcwise homogeneous
On the continuity and monotonicity of restrictions of connected functions
On the continuity of functions.
On the Continuity of Internal Functions
On the continuity of midpoint hall convex set-valued functions.
On the continuity of midpoint hull convex set-valued functions. (Summary).
On the continuity of the elements of the Ellis semigroup and other properties
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 is fixed, we give a necessary and sufficient condition on a point in order that all functions of the Ellis semigroup be continuous at the given point . In the second part, we consider transitive dynamical...
On the continuity of the pressure for monotonic mod one transformations
If is strictly increasing and continuous define . A transformation is called -close to , if for a strictly increasing and continuous function with . It is proved that the topological pressure 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 , if and only if is...
On the convergence and character spectra of compact spaces
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
On the convergence of certain sequences and some applications, II.
On the convergence of implicit Ishikawa iterations with errors to a common fixed point of two mappings in convex metric spaces.