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Uniformly continuous mappings #8

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dan323 opened this issue May 6, 2020 · 0 comments

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dan323 commented May 6, 2020 •

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We need a theory of uniformly continuous mappings to really manage the structure of uniformities:

During the rest of the steps, prove some useful lemmas about (fxg):AxC->BxD the product of 2 functions as a function on products.
Define the uniform continuity for f:X->Y: for any entourage V in Y; (fxf)-``(V) is an entourage in X
Show that they are continous for the associated topologies
Give an example of continuous non uniformly continuous map

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Topological group uniformities. Roelcke uniformity. #4

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Uniformly continuous functions #12

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