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
We consider any . Since is continuous, then for any , we can ...
Assess as a continuous function. The expert examines compactness in topology.