# Topological Spaces and Continuity

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Please see the attached file for the fully formatted problems.

Let be a real valued function on a topological space .

Show that is continuous if and only if for each real number the set and

are open.

Show that is continuous if and only if for each real number the set is

open and is closed.

https://brainmass.com/math/geometry-and-topology/topological-spaces-continuity-164576

#### Solution Summary

Topological spaces and continuity are investigated. The solution is detailed and well presented.

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