Relative Smooth Topological Spaces

B Ghazanfari

doi:10.1155/2009/172917

Abstract

In 1992, Ramadan introduced the concept of a smooth topological space and relativeness between smooth topological space and fuzzy topological space in Chang's (1968) view points. In this paper we give a new definition of smooth topological space. This definition can be considered as a generalization of the smooth topological space which was given by Ramadan. Some general properties such as relative smooth continuity and relative smooth compactness are studied.

Highlights

Let X be a nonempty set and let L, L be two lattice which will be copies of [0, 1] or {0, 1}
The family of all fuzzy sets on X will be denoted by LX Zadeh [1]
We assume that μ as a function from X to L is an observer of X on lattice L and denote [μ] = {λ ∈ LX : λ ⊆ μ}, where λ ⊆ μ implies that λ(x) ≤ μ(x) for all x ∈ X

Summary

Ghazanfari

In 1992, Ramadan introduced the concept of a smooth topological space and relativeness between smooth topological space and fuzzy topological space in Chang’s (1968) view points. In this paper we give a new definition of smooth topological space. This definition can be considered as a generalization of the smooth topological space which was given by Ramadan. Some general properties such as relative smooth continuity and relative smooth compactness are studied

Introduction

Relative Smooth Continuous Maps

The Representation of a Relative Smooth Topology

Relative Smooth Compactness