What is uniformizable space?

Uniformizable Space

In mathematics, a topological space X is uniformizable if there exists a uniform structure on X which induces the topology of X. Equivalently, X is uniformizable if and only if it is homeomorphic to a uniform space (equipped with the topology induced by the uniform structure).

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Some articles on uniformizable space:

Uniformizable Space - Fine Uniformity
... Given a uniformizable space X there is a finest uniformity on X compatible with the topology of X called the fine uniformity or universal uniformity ... A uniform space is said to be fine if it has the fine uniformity generated by its uniform topology ... is characterized by the universal property any continuous function f from a fine space X to a uniform space Y is uniformly continuous ...
Topology of Uniform Spaces - Uniformizable Spaces
... A topological space is called uniformizable if there is a uniform structure compatible with the topology ... Every uniformizable space is a completely regular topological space ... Moreover, for a uniformizable space X the following are equivalent X is a Kolmogorov space X is a Hausdorff space X is a Tychonoff space for any ...

Famous quotes containing the word space:

    No being exists or can exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an effect arising from the first existence of being, because when any being is postulated, space is postulated.
    Isaac Newton (1642–1727)