- #1
St41n
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When we say that a metric space (X,d) induces a topology or "every metric space is a topological space in a natural manner" we mean that:
A metric space (X,d) can be seen as a topological space (X,τ) where the topology τ consists of all the open sets in the metric space?
Which means that all possible open sets (or open balls) in a metric space (X,d) will form the topology τ of the induced topological space?
Is that correct?
A metric space (X,d) can be seen as a topological space (X,τ) where the topology τ consists of all the open sets in the metric space?
Which means that all possible open sets (or open balls) in a metric space (X,d) will form the topology τ of the induced topological space?
Is that correct?