Completely Regular

Some articles on regular, completely regular:

Regular Space - Examples and Nonexamples
... Every such space is regular ... As described above, any completely regular space is regular, and any T0 space that is not Hausdorff (and hence not preregular) cannot be regular ... Most examples of regular and nonregular spaces studied in mathematics may be found in those two articles ...
Tychonoff Space - Properties - Uniform Structures
... In other words, every uniform space has a completely regular topology and every completely regular space X is uniformizable ... Given a completely regular space X there is usually more than one uniformity on X that is compatible with the topology of X ...
Topology of Uniform Spaces - Uniformizable Spaces
... Every uniformizable space is a completely regular topological space ... Conversely, each completely regular space is uniformizable ... A uniformity compatible with the topology of a completely regular space X can be defined as the coarsest uniformity which makes all continuous real-valued functions on X uniformly continuous ...

Famous quotes containing the words regular and/or completely:

    [I]n our country economy, letter writing is an hors d’oeuvre. It is no part of the regular routine of the day.
    Thomas Jefferson (1743–1826)

    Physically there is nothing to distinguish human society from the farm-yard except that children are more troublesome and costly than chickens and calves and that men and women are not so completely enslaved as farm stock.
    George Bernard Shaw (1856–1950)