期刊名称：International Journal of Innovative Research in Science, Engineering and Technology
印刷版ISSN：2347-6710
电子版ISSN：2319-8753
出版年度：2014
卷号：3
期号：12
页码：18070
DOI：10.15680/IJIRSET.2014.0312041
出版社：S&S Publications
摘要：Given a topological space (X,𝒯), we construct uniformities on X compatible with topology of X. Inparticular it is proved that the uniformity 𝒰 generated by continuous real valued functions on X is compatible withtopology of X if and only if X is completely regular.Further it is also proved that the uniformity 𝒰1 generated by continuous bounded real valued functions on X isalso compatible with topology of X under the same hypothesis. In many cases all the uniformities are different. Inparticular all these uniformities coincide for a compact Hausdorff space.
关键词：Completely regular space; sub base for uniformity; continuous real valued function. Subject code;classification in accordance with AMS procedure 54E15.
