DMCA
ON DENSITY TOPOLOGIES WITH RESPECT TO INVARIANT σ-IDEALS (2001)
| Citations: | 2 - 2 self |
BibTeX
@MISC{Hejduk01ondensity,
author = {J. Hejduk},
title = {ON DENSITY TOPOLOGIES WITH RESPECT TO INVARIANT σ-IDEALS},
year = {2001}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Abstract. The density topologies with respect to measure and cate-gory are motivation to consider the density topologies with respect to invariant σ-ideals on R. The properties of such topologies, including the separation axioms, are studied. Notation By R we shall denote the set of all reals numbers and by N the set of positive integers. Let l stand for Lebesgue measure. The capitals L and L denote the σ-algebra of all Lebesgue measurable sets in R and the σ-ideal of all Lebesgue null sets. The natural topology on R is denoted by T0. If T is a topology on R, then we fix the notation: B(T) — the σ-algebra of all Borel sets with respect to T, Ba(T) — the σ-algebra of all sets having the Baire property with respect to T, K(T) — the σ-ideal of all meager sets with respect to T. 2000 Mathematics Subject Classification. 28A05, 54A10. Key words and phrases. Density point, density topology, the separation axioms, in-variant ideals and algebras.
Keyphrases
density topology respect invariant ideal separation axiom positive integer lebesgue measure density topology invariant ideal density point mathematics subject classification borel set natural topology in-variant ideal lebesgue null set baire property key word real number lebesgue measurable set
