July 2020
Intermediate to advanced
384 pages
11h 25m
English
Content preview from A Modern Introduction to Fuzzy Mathematics
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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 
, 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 ...
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