Interpolating functions


Good C., Kopperman R., Yildiz F.

TOPOLOGY AND ITS APPLICATIONS, cilt.158, ss.582-593, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 158 Konu: 4
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.topol.2010.12.002
  • Dergi Adı: TOPOLOGY AND ITS APPLICATIONS
  • Sayfa Sayıları: ss.582-593

Özet

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