10Fuzzy Topology

Geometry and topology are two different branches of mathematics that deal with the same objects. However, as K.D. Joshi [167, p. 67] notes “…if two objects are equivalent for a geometer, they are certainly so for a topologist” and “…two objects which look distinct to a geometer may look the same to a topologist.” In this chapter, we discuss fuzzy topology, and in the next chapter, we explore fuzzy geometry. Since metrics induce topologies, we will start with fuzzy metric spaces.

10.1 Metric and Topological Spaces1

On the line images, the distance from images to images is equal to images. More generally, the distance from images to images is denoted by images and it is equal to

equation

Using the notion of distance, we ...

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