Submaximal space: Difference between revisions
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==Definition== | ==Definition== | ||
===Symbol-free definition=== | |||
A [[topological space]] is termed '''submaximal''' if every subset of it is [[locally closed subset|locally closed]], viz, an intersection of an [[open subset]] and a [[closed subset]]. | A [[topological space]] is termed '''submaximal''' if every subset of it is [[locally closed subset|locally closed]], viz, an intersection of an [[open subset]] and a [[closed subset]]. | ||
Revision as of 19:30, 26 January 2012
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
Definition
Symbol-free definition
A topological space is termed submaximal if every subset of it is locally closed, viz, an intersection of an open subset and a closed subset.
In particular, this means that every dense subset is open.