definition of subbasis of topological space
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of basis of topological space.
Target Context
- The reader will have a definition of subbasis of topological space.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( T\): \(\in \{\text{ the topological spaces }\}\)
\(*S\): \(\subseteq Pow (T)\)
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Conditions:
\(B := \text{ the set of the intersections of each finite subset of } S \in \{\text{ the bases of } T\}\)
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2: Note
When the topology of \(T\) is not determined yet, any \(S\) that contains \(T\) and \(\emptyset\) generates a topology, by the proposition that for any set, any set of subsets with the whole set and the empty set constitutes a subbasis.
