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Topological vectorspaces
... Paul Garrett: Topological vectorspaces (April 20, 2014) subsets. By the Baire category theorem the topology on Cco (R) cannot be complete metric. In particular, it cannot be Fréchet. Nevertheless, the space Ccp (R) and many similarly-constructed spaces do have a reasonable structure, being an asce ...
... Paul Garrett: Topological vectorspaces (April 20, 2014) subsets. By the Baire category theorem the topology on Cco (R) cannot be complete metric. In particular, it cannot be Fréchet. Nevertheless, the space Ccp (R) and many similarly-constructed spaces do have a reasonable structure, being an asce ...
Homework 4
... Read Sections 21, 23, 24, 25 (up to page 160 inclusive). Write solutions to exercises I. Let (X, d) be a metric space and f : X −→ X a continuous map. Prove that the function g : X −→ R defined by g(x) = d(x, f (x)) is a continuous function. (Hint: factor g into a composition of continuous functions ...
... Read Sections 21, 23, 24, 25 (up to page 160 inclusive). Write solutions to exercises I. Let (X, d) be a metric space and f : X −→ X a continuous map. Prove that the function g : X −→ R defined by g(x) = d(x, f (x)) is a continuous function. (Hint: factor g into a composition of continuous functions ...