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Tag Archives: complete metric spaces
Topology: More on Compact Spaces
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
Topology: Complete Metric Spaces
[ 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
Posted in Notes
Tagged advanced, cauchy sequences, complete metric spaces, completion, metric spaces, topology, universal properties
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