Interpolating functions

Good C., Kopperman R., Yildiz F.

TOPOLOGY AND ITS APPLICATIONS, vol.158, no.4, pp.582-593, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 158 Issue: 4
  • Publication Date: 2011
  • Doi Number: 10.1016/j.topol.2010.12.002
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.582-593
  • Hacettepe University Affiliated: Yes

Abstract

Let X, Y be sets with quasiproximities (sic)x and (sic)y (where A (sic) B is interpreted as "B isa neighborhood of A"). Let f.g : X -> Y be a pair of functions such that whenever C (sic)y D. then f(-1) vertical bar C vertical bar (sic)x g(-1)vertical bar D vertical bar. We show that there is then a function h : X -> Y such that whenever C (sic)y D. then f(-1)vertical bar C vertical bar (sic)x h(-1)vertical bar D vertical bar, h(-1)vertical bar C vertical bar (sic)x h(-1)vertical bar D vertical bar and h(-1)vertical bar C vertical bar (sic)x g(-1)vertical bar D vertical bar. Since any function It that satisfies h(-1) vertical bar C vertical bar (sic)x h(-1)vertical bar D vertical bar whenever C (sic)y D, is continuous, many classical "sandwich" or "insertion" theorems are corollaries of this result. The paper is written to emphasize the strong similarities between several concepts