Advertisement

Functional Separation Conditions

  • I. M. James
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Let H, K be a disjoint pair of subsets of the topological space X. Chapter 6 is concerned with the question of whether H and K can be separated: Do there exist open neighbourhoods U, V of H, K, respectively, which are also disjoint? The present chapter is concerned with the question of whether H and K can be functionally separated: Does there exist a continuous real-valued function α: X →I such that α = 0 throughout H and α = 1 throughout K? The latter condition implies the former since we can take U = α-1[0,1-2, V = α-1(1-2, 1].

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • I. M. James
    • 1
  1. 1.Mathematical InstituteUniversity of OxfordOxfordEngland

Personalised recommendations