Continuity Enabling Structures

Louis Nel
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Louis Nel: Carleton University, School of Mathematics and Statistics

Chapter Chapter 3 in Continuity Theory, 2016, pp 53-92 from Springer

Abstract: Abstract Continuous mappings are defined via functions that preserve convergence. In this chapter we discuss selected classes of spaces that makes the definition of convergence possible and therefore also the definition of continuous mapping. There is no attempt to be encyclopedic. It will be seen that for every kind of space there are certain auxiliary concepts that enable expression of continuity in various equivalent ways. The filter concept is one such auxiliary. We introduce it even for real intervals, where sequential convergence is adequate, but where students can get used to it in a familiar environment.

Keywords: Convergence Spaces; Convergent Filter; Neighborhood Filter; Tail Filter; Filter Base (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-31159-3_3

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