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Unit 8: The Product Topology

3. Prove that the product of any finite number of indiscrete spaces is an indiscrete space. Notes
4. For each i  N, let C be a closed subset of a topological space (X , T ). Prove that Õ ¥ i 1 C is
i i i = i
a closed subset of Õ ¥ i 1 (X , T ).
=
i
i
5. Let (X , T ), i  N, be a countably infinite family of topological spaces. Prove that each
i i
(X , T ) is homeomorphic to a subspace of Õ ¥ i 1 (X , T ).
i i = i i
8.5 Further Readings

Books Dixmier, General Topology (1984).

James R. Munkres, Topology, Second Edition, Pearson Prentice Hall.

Online links mathworld.wolfram.com/product topology.html
www.history.mcs.st-and.ac.uk/~john/MT4522/Lectures/L1.5.html

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