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On the concept of generalization of I-density points

100%

Hejduk J. , Wiertelak R.

tom Vol. 43, no. 6

803--811

This paper deals with essential generalization of I-density points and I-density topology. In particular, there is an example showing that this generalization of I-density point yields the stronger concept of density point than the notion of I(J )-density. Some properties of topologies generated by operators related to this essential generalization of density points are provided.

On the comparison of the density type topologies generated by sequences and by functions

80%

Filipczak M. , Filipczak T.

tom Vol. 49, [Z] 2

161-170

In the paper we investigate density type topologies generated by functions f satisfying condition [formula] which are not generated by any sequence.

Ψ I -density topology

80%

Łazarow E. , Vizváry A.

tom Vol. 15

67--80

The purpose of this paper is to study the notion of a Ψ I-density point and Ψ I -density topology, generated by it analogously to the classical I-density topology on the real line. The idea arises from the note by Taylor [3] and Terepeta and Wagner-Bojakowska [2].

On homeomorphisms of the density type topologies

80%

Filipczak M. , Hejduk J. , Wilczyński W.

Commentationes Mathematicae

2005

tom 45

nr 2

This paper is dealing of the homeomorphisms of the density type topologies introduced in [3].

On the convergence of sequences of functions which are discontinuous on countable sets

70%

Grande Z. , Strońska E.

tom Vol. 11, nr 2

247-259

Let (X, Tx) be a topological space and let (Y, dy) be a metric space. For a function f : X → y denote by C(f) the set of all continuity points of f and by D(f) = X\C(f) the set of all discontinuity points of f. Let C(X,Y) = {f : X → Y; f is continuous}, H(X, Y) = {f: X →Y; D{f) is countable}, H1(X, Y) = {f: X → Y; ∃h ∈c(x,Y) {x; f(x) ≠ h{x)} is countable}, and H2(X, Y) = H(X, Y) ∩ H1(X, Y). In this article we investigate some convergences (pointwise, uniform, quasiuniform, discrete and transfinite) of sequences of functions from H(X, Y), H1(X, Y) and H2(X, Y).

On the product of two functions which are approximately continuous and approximately regulated

60%

Grande M.

2006

tom Vol. 39, nr 2

327-334

In this article we investigate the products of two unilaterally approximately continuous and simultaneously approximately regulated functions. In particular we prove some necessary conditions satisfied by the products of two such functions and a sufficient condition ensuring that a function is the product of two such functions.