Answer to Question #117897 in Differential Geometry | Topology for Sheela John

Question #117897
Prove or disprove any metric defined on X(#0) induces a topology on X
1
Expert's answer
2020-05-25T15:46:54-0400

disprove:

for a set A such that |A| >1, for a,b"\\in" A

let a is not equal to b and d(a,b)=m , then,

for the ball B(m/2,a) which has radius m/2 does not contain 'b', that is

b "\\notin" B(m/2,a)

this implies B(m/2,a) is neither equal to "\\varnothing" nor equal to set A

that means it does not induce a trivial topology.


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