World Library  
Flag as Inappropriate
Email this Article

Completely uniformizable space

Article Id: WHEBN0027351720
Reproduction Date:

Title: Completely uniformizable space  
Author: World Heritage Encyclopedia
Language: English
Subject: Uniform space, Completely metrizable space
Publisher: World Heritage Encyclopedia

Completely uniformizable space

In mathematics, a topological space (X, T) is called completely uniformizable[1] (or Dieudonné complete[2] or topologically complete[3]) if there exists at least one complete uniformity that induces the topology T. Some authors additionally require X to be Hausdorff. The term topologically complete is also often used for complete metrizability, which is a stronger condition than complete uniformizability.


Every metrizable space is paracompact, hence completely uniformizable. As there exist metrizable spaces that are not completely metrizable, complete uniformizability is a strictly weaker condition than complete metrizability.

See also



This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.