Open Functions and Closed Functions
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.
KeywordsTopological Space Open Function Open Neighbourhood Direct Image Continuous Injection
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