Nearness-based topology. (English) Zbl 0993.54006

Dobrakovová, Jana

Tatra Mt. Math. Publ. 21, 163-169 (2001).

A binary fuzzy relation \(N\) on a universe \(X\) is called a nearness on \(X\) if \(N(x,x)=1 (x\in X)\), \(N(x,y)=N(y,x) (x,y \in X)\), and for every \(\varepsilon >0\) there exists \(\delta <1\) such that \(N(x,y)>\delta \) implies \(|N(x,z)- N(y,z) |< \varepsilon (x,y,z \in X).\) The corresponding notions of \(N\)-topology, \(N\)-convergence, \(N\)-continuity are investigated, and a fixed point theorem on \(N\)-topological space is established.

Reviewer: Endre Pap (Novi Sad)

MSC:

54A40	Fuzzy topology
54E17	Nearness spaces

Keywords:

nearness; \(N\)-topology