Uniform isomorphism

In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces that respects uniform properties.

Definition

A function f between two uniform spaces X and Y is called a uniform isomorphism if it satisfies the following properties

If a uniform isomorphism exists between two uniform spaces they are called uniformly isomorphic or uniformly equivalent.

Examples

The uniform structures induced by equivalent norms on a vector space are uniformly isomorphic.

gollark: How efficiency of you to randomly generate inefficient code then uninefficient it later.
gollark: All conversations are about Macron.
gollark: Yes.
gollark: <@750944057794101298>
gollark: The closest is probably coral, who is studying to be an electrical engineer.

See also

  • Homeomorphism—an isomorphism between topological spaces
  • Isometric isomorphism—an isomorphism between metric spaces

References

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