Tag Archives: subbases

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: Subspaces

Posted on January 25, 2013 by limsup

First, suppose (X, d) is a metric space. If Y is a subset of X, then one can restrict the metric to , i.e. for any , we set d’(y, y’) := d(y, y’). It’s not hard to show that the resulting function is a metric on Y. … Continue reading →

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Topology: Bases and Subbases

Posted on January 21, 2013 by limsup

Bases Recall that though a subring or ideal of a ring may be rather huge, it often suffices to specify just a few elements which will generate the subring or ideal. Likewise, in a topology,  one can specify a few … Continue reading →

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