Box topology
From Maths
Revision as of 10:19, 26 September 2016 by Alec (Talk | contribs) (Created page with "{{Stub page|grade=B|msg=Not that important because we have the product topology page, however it should be a slightly bigger stub page!}} ==Definition== Let {{M|\big((X_\alpha...")
Stub grade: B
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Not that important because we have the product topology page, however it should be a slightly bigger stub page!
Definition
Let ((Xα,Jα))α∈I be an arbitrary family of topological spaces. The box topology is the topology generated by the following basis[1]:
- B:={∏α∈IUα | (Uα)α∈I∈∏α∈IJα} - the basis consisting of all Cartesian products of all open sets from ((Xα,Jα))α∈I[Note 1]
TODO: Check this expression
Notes
- ↑ Badly phrased, it should mean all tuples of the form (Uα)α∈I where ∀α∈I[Uα∈Jα]
References
| |||||||||||||||||||||||
