July 2020
Intermediate to advanced
384 pages
11h 25m
English
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.
On the line
, the distance from
to
is equal to
. More generally, the distance from
to
is denoted by
and it is equal to
Using the notion of distance, we ...