Total Boundedness

Some articles on total boundedness, boundedness:

Totally Bounded Space - Use of The Axiom of Choice
... The properties of total boundedness mentioned above rely in part on the axiom of choice ... In the absence of the axiom of choice, total boundedness and precompactness must be distinguished ... That is, we define total boundedness in elementary terms but define precompactness in terms of compactness and Cauchy completion ...
Totally Bounded Space - Relationships With Compactness and Completeness
... There is a nice relationship between total boundedness and compactness A uniform space is compact if and only if it is both totally bounded and Cauchy complete ... spaces to arbitrary spaces we must replace boundedness with total boundedness (and also replace closedness with completeness) ... There is a complementary relationship between total boundedness and the process of Cauchy completion A uniform space is totally bounded if and only if its Cauchy completion is totally bounded ...

Famous quotes containing the word total:

    Throughout human history, the apostles of purity, those who have claimed to possess a total explanation, have wrought havoc among mere mixed-up human beings.
    Salman Rushdie (b. 1948)