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Tag Archives: homeomorphisms
Topology: Topological Groups
This article assumes you know some basic group theory. The motivation here is to consider groups whose underlying operations are continuous with respect to its topology. Definition. A topological group G is a group with an underlying topology such that: the … Continue reading
Posted in Notes
Tagged advanced, compact sets, connected components, groups, homeomorphisms, separation axioms, topological groups, topology
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Topology: Subspaces
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
Posted in Notes
Tagged advanced, bases, clopen sets, homeomorphisms, metric spaces, subbases, subspaces, topology
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