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totally bounded uniform space

Defines: 
totally bounded, totally bounded uniformity
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

54E35 no label found

Comments

Sorry, my wrong LaTeX. I repeat the comment again.

Minimus Heximus user of math.stackexchange.com has given in his answer an other definition:

(X,?)X?(X,\mathcal{D}) is totally boundedPlanetmathPlanetmath, when for each entourage D?D?D\in\mathcal{D}, there are x1,,xnXsubscriptx1normal-…subscriptxnXx_{1},...,x_{n}\in X with D[x1]D[xn]=XDsubscriptx1normal-…DsubscriptxnXD[x_{1}]\cup...\cup D[x_{n}]=X.

Minimus Heximus has proved that his definition follows from PlanetMath definition.

Does the converse hold? Is the PlanetMath’s definition a consequence of Minimus Heximus’s definition? Or is there a counter-example?

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