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Tag Archives: closures
Topology: Product Spaces (II)
The Box Topology Following an earlier article on products of two topological spaces, we’ll now talk about a product of possibly infinitely many topological spaces. Suppose is a collection of topological spaces indexed by I, and we wish to define … Continue reading
Topology: Interior
Let Y be a subset of a topological space X. In the previous article, we defined the closure of Y as the smallest closed subset of X containing Y. Dually, we shall now define the interior of Y to be the largest open subset contained in … Continue reading
Posted in Notes
Tagged advanced, boundaries, closures, interiors, product topology, subspaces, topology
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Topology: Closure
Suppose Y is a subset of a topological space X. We define cl(Y) to be the “smallest” closed subset containing Y. Its formal definition is as follows. Let Σ be the collection of all closed subsets containing Y. Note that , so Σ is not empty. … Continue reading
Posted in Notes
Tagged advanced, closed balls, closed subsets, closures, open balls, points of accumulation, product topology, topology
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