<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We study the properties of category density topology of the plane generated by a restricted convergence in the category of double sequences of characteristic functions <disp-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/v10127-010-0019-4#0005_graphic1.png"></inline-graphic></disp-formula> and more interesting topology generated by a strict convergence in the category of the same sequences, which is a natural modification of a previous one. Similar problems for measure density were considered in [M. Filipczak, W. Wilczy´nski: <italic>Strict density topology on the plane. Measure case </italic>(in preparation)].</p></abstract>

We study the properties of category density topology of the plane generated by a restricted convergence in the category of double sequences of characteristic functions  and more interesting topology generated by a strict convergence in the category of the same sequences, which is a natural modification of a previous one. Similar problems for measure density were considered in [M. Filipczak, W. Wilczy´nski: Strict density topology on the plane. Measure case (in preparation)].

Strict density topology of the plane. category case

Faculty of Mathematics and Computer Science University of Łódź Banacha 22 PL–90-238 Łódź POLAND

Faculty of Mathematics and Computer Science University of Łódź Banacha 22 PL–90-238  Łódź POLAND

Tatra Mountains Mathematical Publications

{"article-title":"Strict density topology of the plane. category case"}

We study the properties of category density topology of the plane generated by a restricted convergence in the category of double sequences of characteristic...

Strict density topology of the plane. category case

Publié en ligne: 13 nov. 2012

Pages: 55 - 64

DOI: https://doi.org/10.2478/v10127-010-0019-4

Mots clés
category density of the plane, convergence in the restricted sense, separation axioms.

This content is open access.

Strict density topology of the plane. category case

Publié en ligne: 13 nov. 2012

Pages: 55 - 64

DOI: https://doi.org/10.2478/v10127-010-0019-4

Mots cléscategory density of the plane, convergence in the restricted sense, separation axioms.

This content is open access.

Mots clés
category density of the plane, convergence in the restricted sense, separation axioms.