<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The paper is concerned with homeomorphisms on topological spaces (ℝ<italic>, T</italic>ƒ<italic></italic>), where <italic>T</italic>ƒ is a generalization of the density topology generated by a function ƒ. It is shown that the density topology is not homeomorphic with any other topology <italic>T</italic>ƒ and that, under some assumptions, homeomorphic ƒ-density topologies have to be comparable.</p></abstract>

The paper is concerned with homeomorphisms on topological spaces (ℝ, Tƒ), where Tƒ is a generalization of the density topology generated by a function ƒ. It is shown that the density topology is not homeomorphic with any other topology Tƒ and that, under some assumptions, homeomorphic ƒ-density topologies have to be comparable.

On homeomorphisms of density type topologies generated by functions

Faculty of Mathematics and Computer Sciences Łódź University ul. Stefana Banacha 22, PL–90-238 Łódź POLAND

Institute of Mathematics Łódź Technical University ul. W´olcza´nska 215 PL–93-005 Łódź  POLAND

Tatra Mountains Mathematical Publications

{"article-title":"On homeomorphisms of density type topologies generated by functions"}

The paper is concerned with homeomorphisms on topological spaces (ℝ, Tƒ), where Tƒ is a generalization of the density topology generated by a function ƒ. It is...

On homeomorphisms of density type topologies generated by functions

Published Online: Nov 13, 2012

Page range: 7 - 13

DOI: https://doi.org/10.2478/v10127-010-0014-9

Keywords
density point, density topology, homeomorphism.

This content is open access.

On homeomorphisms of density type topologies generated by functions

Published Online: Nov 13, 2012

Page range: 7 - 13

DOI: https://doi.org/10.2478/v10127-010-0014-9

Keywordsdensity point, density topology, homeomorphism.

This content is open access.

Keywords
density point, density topology, homeomorphism.