Tag Archives: complete metric spaces

Topology: More on Compact Spaces

Posted on February 26, 2013 by limsup

In the previous article, we defined compact spaces as those where every open cover has a finite subcover, i.e. if then we can find a finite set of indices such that On an intuitive level, one should imagine a compact … Continue reading →

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Topology: Complete Metric Spaces

Posted on February 21, 2013 by limsup

[ This article was updated on 8 Mar 13; the universal property is now in terms of Cauchy-continuous maps. ]  On an intuitive level, a complete metric space is one where there are “no gaps”. Formally, we have: Definition. A … Continue reading →

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