Some Topology Problems and Solutions | General Topology | Empty SetTutorials : Fri - in CM G. Beck -at- hw. Announcements Regular lectures completed : Just to clarify, the regular lectures have now been completed. The only scheduled meeting times during weeks 11 and 12 are the revisions lectures, explained below. During weeks 11 and 12 we will not meet during lecture times on Tuesdays or Fridays, or during the tutorial times. Posted 18 Nov.
X. Oliver - Variational approach to topological optimization problems
Munkres (2000) Topology with Solutions
True or false? Suppose that, whenever F is closed in X, the image f F is closed in Y. Then, whenever U is open in X, f U is open in Y. Solution: a True: every subspace is closed. This statement does hold whenever f is bijective. Options for a counterexample include: any map between cofinite topological spaces preserves closed, i. Note that the converse is not true either: a map that preserves open subspaces under direct image does not necessarily preserve closed subspaces.
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