Definition:Sub-Basis/Synthetic Sub-Basis
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Definition
Let $S$ be a set.
A synthetic sub-basis on $S$ is any subset $\SS \subseteq \powerset S$ of the power set of $S$.
Also known as
Some sources do not distinguish between a synthetic sub-basis and an analytic sub-basis, and instead use the definition for an analytic sub-basis and just call that a sub-basis.
Some sources do not hyphenate sub-basis but instead render it as subbasis.
Some sources use the term sub-base (or subbase).
Also see
- Definition:Topology Generated by Synthetic Sub-Basis
- Definition:Analytic Sub-Basis
- Definition:Basis (Topology)
Linguistic Note
The plural of sub-basis is sub-bases.
This is properly pronounced sub-bay-seez, rather than sub-bay-siz, deriving as it does from the Greek plural form of nouns ending -is.
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: $3.3$: Sub-bases and weak topologies