# continuous function

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Topology- Compactness

Please do the problem #1. My textbook is Topology by James R. Munkres.

The following are the contents covered in class so far. Do not use any knowledge exceeding them.

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Sep-08-09 Session 1 Metric spaces and continuous maps.

Sep-10-09 Session 2 Topological spaces and continuous maps.

Sep-15-09 Session 3 Examples of topologies.

Sep-17-09 Session 4 Closures, interiors, the Hausdorff axiom. Infinite products of spaces.

Sep-22-09 Session 5 The quotient topology. Surfaces.

Sep-24-09 Session 6 Connectedness and path connectedness.

Sep-29-09 Session 7 Compactness.

Oct-01-09 Session 8 Digression: knots, surfaces and all that

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##### Solution Summary

Assess as a continuous function. The expert examines compactness in topology.

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Proof:

We consider any . Since is continuous, then for any , we can ...

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