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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.

Keywords

Topological Space Open Function Open Neighbourhood Direct Image Continuous Injection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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