A 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: Definition
For any set, S, a set of some subsets (called open sets), O, such that 1) \(\emptyset \in O\) and \(S \in O\) 2) for any \(U_1 \in O\) and any \(U_2 \in O\), \(U_1 \cap V_2 \in O\) 3) for any \(U_\alpha \in O\) where \(\alpha \in A\) where A is any index set not necessarily countable, \((\cup_\alpha U_\alpha) \in O\)
