<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Let <italic>Tψ </italic>be a <italic>ψ</italic>-density topology for a fixed function <italic>ψ</italic>. For any topological space <italic>X </italic>with the topology <italic>τ </italic>we will consider the family C (<italic>X, </italic>ℝ<italic>ψ</italic>) of all continuous functions <italic>f </italic>from (<italic>X, τ</italic>) into (ℝ<italic>, Tψ</italic>). The main aim of this paper is to investigate when <italic>C </italic>(<italic>X, </italic>ℝ<italic>ψ</italic>) is a ring. This article is based on the results achieved by M. Knox [<italic>A characterization of rings of density continuous functions</italic>, Real Anal. Exchange <bold>31 </bold>(2005), 165-177].</p></abstract>

Let Tψ be a ψ-density topology for a fixed function ψ. For any topological space X with the topology τ we will consider the family C (X, ℝψ) of all continuous functions f from (X, τ) into (ℝ, Tψ). The main aim of this paper is to investigate when C (X, ℝψ) is a ring. This article is based on the results achieved by M. Knox [A characterization of rings of density continuous functions, Real Anal. Exchange 31 (2005), 165-177].

A new approach to ψ-continuity

Center of Mathematics and Physics Łódź Technical University al. Politechniki 11 PL–90-924 Łódź POLAND

Tatra Mountains Mathematical Publications

{"article-title":"A new approach to ψ-continuity"}

Let Tψ be a ψ-density topology for a fixed function ψ. For any topological space X with the topology τ we will consider the family C (X, ℝψ) of all continuous...

A new approach to ψ-continuity

Published Online: Nov 12, 2012

Page range: 107 - 117

DOI: https://doi.org/10.2478/v10127-009-0011-z

Keywords
density point, density topology, ψ-density topology, ring, lattice

This content is open access.

A new approach to ψ-continuity

Published Online: Nov 12, 2012

Page range: 107 - 117

DOI: https://doi.org/10.2478/v10127-009-0011-z

Keywordsdensity point, density topology, ψ-density topology, ring, lattice

This content is open access.

Keywords
density point, density topology, ψ-density topology, ring, lattice