definition of topology
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of set.
Target Context
- The reader will have a definition of topology.
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:
\( S\): \(\in \{\text{ the sets }\}\)
\(*O\): \(\subseteq Pow (S)\)
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Conditions:
1) \(\emptyset \in O\) and \(S \in O\)
\(\land\)
2) for any \(U_1 \in O\) and any \(U_2 \in O\), \(U_1 \cap U_2 \in O\)
\(\land\)
3) for any \(U_j \in O\) where \(j \in J\) where \(J\) is any index set not necessarily countable, \((\cup_{j \in J} U_j) \in O\)
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Each element of \(O\) is called "open subset".
