homeomorphism between Boolean spaces
We start with two general remarks.
If are Boolean spaces, then a bijection is homeomorphism iff it maps clopen sets to clopen sets.
Once more, one direction is clear. Now, suppose maps clopen sets to clopen sets. Since is zero-dimensional, is continuous by the first proposition. Since is compact and Hausdorff, is a homeomorphism by the second proposition. ∎
|Title||homeomorphism between Boolean spaces|
|Date of creation||2013-03-22 19:09:04|
|Last modified on||2013-03-22 19:09:04|
|Last modified by||CWoo (3771)|