Isolated point: Difference between revisions
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A point in a [[topological space]] is said to be an '''isolated point''' if the singleton set comprising that point, is an [[open subset]]. | A point in a [[topological space]] is said to be an '''isolated point''' if the singleton set comprising that point, is an [[open subset]]. | ||
Often, we talk of isolated points in a ''subset'' of a topological space. An isolated point in a subset is simply an isolated point in the above sense, with respect to the subset endowed with the [[subspace topology]]. | Often, we talk of isolated points in a ''subset'' of a topological space. An isolated point in a subset is simply an isolated point in the above sense, with respect to the subset endowed with the [[subspace topology]]. Equivalently, the point is in the subset but is not a [[limit point]] of the subset. | ||
Latest revision as of 19:47, 11 May 2008
This article is about a basic definition in topology.
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Definition
A point in a topological space is said to be an isolated point if the singleton set comprising that point, is an open subset.
Often, we talk of isolated points in a subset of a topological space. An isolated point in a subset is simply an isolated point in the above sense, with respect to the subset endowed with the subspace topology. Equivalently, the point is in the subset but is not a limit point of the subset.