# continuous function

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.

(If you have more questions about my posting, communicate through the Message Center.)

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

https://brainmass.com/math/geometry-and-topology/topology-compactness-continuous-function-273970

#### Solution Preview

Proof:

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

#### Solution Summary

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