The interior operation in $f$-density topology

In: Tatra Mountains Mathematical Publications, vol. 35, no. 1

Małgorzata Filipczak - Elżbieta Wagner-Bojakowska

Detaily:

Rok, strany: 2007, 51 - 64

Kľúčové slová:

density point, density topology, $f$-density point, $f$-density topology, interior operation

O článku:

We give a characterization of the interior for an arbitrary subset $A$ of the real line in $f$-density topology generated by the operator $Φ_f$, for which Lebesgue Density Theorem does not hold. We prove that for an arbitrary set $AsubsetBbb R$ its interior in $f$-density topology equals $Acap Φ_f^β(B)$, where $B$ is a measurable kernel of $A$ and $β$ is some countable ordinal. Moreover, each natural number $n$ realizes the interior of $A$ for some measurable $A$.

Ako citovať:

ISO 690:

Filipczak, M., Wagner-Bojakowska, E. 2007. The interior operation in $f$-density topology. In Tatra Mountains Mathematical Publications, vol. 35, no.1, pp. 51-64. 1210-3195.

APA:

Filipczak, M., Wagner-Bojakowska, E. (2007). The interior operation in $f$-density topology. Tatra Mountains Mathematical Publications, 35(1), 51-64. 1210-3195.