If f : (M,) (N,) is a continuous function between two metric spaces, then f :

If f : (M,ρ) −→ (N,σ) is a continuous function between two metric spaces, then f : (M, τρ ) −→ (N, τσ) is a continuous function between the topological spaces with the topologies induced by the metrics.

how can I prove it rigorously?

 

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Given any open set in N we have to show its inverse image under f is open i... View the full answer