More Properties of Semi-Linear Uniform Spaces

Abstract

In this paper we shall generalize the definition given in [1] for Lipschitz condition and contractions for functions on a non-metrizable space, besides we shall give more properties of semi-linear uniform spaces.

Fixed Point in Semi-linear Uniform Spaces and Convex Metric Spaces

“…By mid point property let w 1 be such that d(x, w 1 ) = d(w 1 , z) = 1 2 d (x, z). So we continuo this way to obtained w 1 , w 2 , ...w n such that d (x, w n ) = 1 2 n d (x, z) < ε. So {w n } converges to x.…”

“…If f is a contraction from a complete semi-linear uniform space (X, Γ) to it self, is f has a unique fixed point. Finally S. Alhihi and M. AlFayaad in [2] gave some topological properties of semi-linear uniform spaces.…”

“…In [2], S. Alhihi and M. Fayyad showed that every semi-linear uniform space induced a Tychonoff space (X, T Γ ) where T Γ induced by local base B x = {B(x, U ) : U ∈ Γ} where B(x, U ) = {y : (x, y) ∈ U }. For more topological properties of T Γ we refer the reader to [2].…”