Subbasis for a topological space
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This article is about a basic definition in topology.
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A subbasis for a topological space is a collection of open subsets of the topological space such that the following equivalent conditions hold:
- The set of subsets obtained by taking finite (possibly empty) intersections of these, form a basis for the topological space
- Every open subset is a countable union of finite intersections of these
- The topology on the space is the coarsest topology for which the given subsets are all open
No constraints are there for a collection of subsets to form a subbasis.