Sufficiently Near Sets of Neighbourhoods

  • James F. Peters
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6954)

Abstract

The focus of this paper is on sets of neighbourhoods that are sufficiently near each other as yet another way to consider near sets. This study has important implications in M. Katětov’s approach to topologising a set. A pair of neighbourhoods of points are sufficiently near, provided that the C̆ech distance between the neighbourhoods is less than some number ε. Sets of neighbourhoods are sufficiently near, provided the C̆ech distance between the sets of neighbourhoods is less than some number ε.

Keywords

Approach space C̆ech distance collection ε-near collections merotopy near sets neighbourhood topology 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • James F. Peters
    • 1
  1. 1.Computational Intelligence Laboratory, Department of Electrical & Computer EngineeringUniv. of ManitobaWinnipegCanada

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