Causal sets: Difference between revisions
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In mathematics, if a [[topological space]] <math>X</math> is said to be '''complete''', it may mean: | |||
* that <math>X</math> has been equipped with an additional [[Cauchy space]] structure which is complete, | |||
** e. g., that it is a [[complete uniform space]] with respect to an aforementioned uniformity, | |||
*** e. g., that it is a [[complete metric space]] with respect to an aforementioned metric; | |||
* or that <math>X</math> has some topological property related to the above: | |||
** that it is [[completely metrizable]] (often called ''(metrically) topologically complete''), | |||
** or that it is [[completely uniformizable]] (also called ''topologically complete'' by some authors). | |||
{{disambiguation}} |
Revision as of 16:58, 14 January 2014
In mathematics, if a topological space is said to be complete, it may mean:
- that has been equipped with an additional Cauchy space structure which is complete,
- e. g., that it is a complete uniform space with respect to an aforementioned uniformity,
- e. g., that it is a complete metric space with respect to an aforementioned metric;
- e. g., that it is a complete uniform space with respect to an aforementioned uniformity,
- or that has some topological property related to the above:
- that it is completely metrizable (often called (metrically) topologically complete),
- or that it is completely uniformizable (also called topologically complete by some authors).