Uniformspaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and uniform convergence.
Uniform spaces may be defined alternatively and equivalently using systems of pseudometrics, an approach which is often useful in functional analysis.
Every uniform space is a completely regular topological space, and conversely, every completely regular space can be turned into a uniform space (often in many ways) so that the induced topology coincides with the given one.
In the mathematical field of topology a homeomorphism or topological isomorphism (from the Greek words homeos = identical and morphe = shape) is a special isomorphism between topological spaces which respects topological properties.
Every uniformisomorphism and isometric isomorphism is a homeomorphism.
uniformisomorphism is an isomorphism between uniform spaces
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