Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Uniform isomorphism
Summary
In the mathematical field of topology a uniform isomorphism or is a special isomorphism between uniform spaces that respects uniform properties. Uniform spaces with uniform maps form a . An isomorphism between uniform spaces is called a uniform isomorphism.
A function between two uniform spaces and is called a uniform isomorphism if it satisfies the following properties
is a bijection
is uniformly continuous
the inverse function is uniformly continuous
In other words, a uniform isomorphism is a uniformly continuous bijection between uniform spaces whose inverse is also uniformly continuous.
If a uniform isomorphism exists between two uniform spaces they are called or .
Uniform embeddings
A is an injective uniformly continuous map between uniform spaces whose inverse is also uniformly continuous, where the image has the subspace uniformity inherited from
The uniform structures induced by equivalent norms on a vector space are uniformly isomorphic.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.