<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

Published Online: Nov 13, 2012

Page range: 55 - 64

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

Keywords
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

Published Online: Nov 13, 2012

Page range: 55 - 64

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

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

This content is open access.

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