A new note on asymmetric metric spaces


Ince Dagci F., Misirlioglu T., Akalli H., Kočinac L. D.

6th International Conference of Mathematical Sciences, ICMS 2022, Hybrid, Istanbul, Türkiye, 20 - 24 Temmuz 2022, cilt.2879 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 2879
  • Doi Numarası: 10.1063/5.0175842
  • Basıldığı Şehir: Hybrid, Istanbul
  • Basıldığı Ülke: Türkiye
  • Anahtar Kelimeler: Asymmetric, backward convergence., forward convergence
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

If the classical metric axioms on a set X are changed by disregarding the case that d(x, y)=0 implies x=y, the general properties for metric spaces will easily be extended. In this case d is called a pseudo-metric. Neverthless, if the necessity of the symmetry of d is disregarded, the proper extensions of metric consequences are not evident at all. A pseudo-asymmetric on a non-empty set X is a non-negative real-valued function p on X×X such that for x, y, z∈X we have p(x, x)=0 and p(x, y)≤p(x, z)+p(z, y). If p satisfies the additional condition that p(x, y)=0 implies x=y, then p is an asymmetric metric on X. A set with an asymmetric metric is called an asymmetric space. Since symmetry necessity is not satisfied, there are two kinds of open balls, namely forward balls and backward balls. As a result, there are two kinds of topological notions. Here we give some theorems related to convergence of sequences of functions and forward and backward total boundedness on asymmetric spaces.