Question

Every metric space is a topological space true or false

Answer 1

Answer:

False

A metric space is not a topological space. However, every metric space gives rise to a topological space in a rather natural way.

Answer 2

Answer: A topological space which can arise in this way from a metric space is called a metrizable space; see the article on metrization theorems for further details. A sequence ( ) in a metric space is said to converge to the limit iff for every , there exists a natural number N such that for all .