Open Functions and Closed Functions

  • Ioan Mackenzie James
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

In Chapter 2 we studied functions from one topological space into another which are structure-preserving in the inverse image sense. In the present chapter we shall primarily be concerned with functions which are structure-preserving in the direct image sense. Specifically, we shall be concerned with functions which send open sets to open sets, and with functions which send closed sets to closed sets. Usually, but not invariably, the functions will be required to be continuous as well.

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Copyright information

© Springer-Verlag London 1999

Authors and Affiliations

  • Ioan Mackenzie James
    • 1
  1. 1.Mathematical InstituteOxford UniversityOxfordUK

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