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Topology

Notes Regular: Let X be a topological space where one-point sets are closed. Then X is regular if a point
and a disjoint closed set can be separated by open sets.

26.4 Review Questions

1. If a separable space is also metrizable, then prove that the space has a countable base.
2. Show that any finite subset of metrizable space is always discrete.
3. Show that a topological space X is metrizable  there exists a homeomorphism of X onto
a subspace of some metric space Y.
4. A compact Hausdorff space is separable and metrizable if it is:
(a) second countable (b) not second countable
(c) first countable (d) none

26.5 Further Readings

Books Lawson, Terry, Topology : A Geometric Approach. New York, NY: Oxford University
Press, 2003.
Robert Canover, A first course in topology. The Williams and Wilkins Company,
1975.

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