The Concept of Oscillation in Uniform Spaces

ŞİMŞEK N., Alizade B.

Azerbaijan Journal of Mathematics, cilt.12, sa.2, ss.184-189, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 2
  • Basım Tarihi: 2022
  • Dergi Adı: Azerbaijan Journal of Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.184-189
  • Anahtar Kelimeler: uniform spaces, the oscillation of a function, fundamentality, base limit
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

This article introduces the concept of the oscillation in uniform spaces, which is generalization of the similar concept in Banach (or metric) spaces. In terms of this concept, we give a definition for the fundamentality of function with respect to a base and prove that it is equivalent to the existence of the limit of function with respect to a base in sequentially complete uniform spaces.