subbase
Sign in to saveIn topology in mathematics, a subbase (or subbasis, prebase, prebasis) for the topology of a topological space is a subcollection B of \tau that generates \tau, in the sense that \tau is the smallest topology containing B as open sets. A slightly different definition is used by some authors, and there are other useful equivalent formulations of the definition; these are discussed below.
~13 min read
Encyclopedic overview
9 sectionsContents
- Definition
- Alternative definition
- Examples
- Results using subbases
- Alexander subbase theorem
- See also
- Notes
- Citations
- References
In topology in mathematics, a subbase (or subbasis, prebase, prebasis) for the topology of a topological space is a subcollection B of \tau that generates \tau, in the sense that \tau is the smallest topology containing B as open sets. A slightly different definition is used by some authors, and there are other useful equivalent formulations of the definition; these are discussed below.
Subbase is a weaker notion than that of a base for a topology.
Excerpted from Wikipedia’s “subbase” article, available under the CC BY-SA 4.0 licence.