testing for continuity via basic open sets
First, note that , since every basic open set is open, and every element in a subbasis is in the basis it generates. We next prove .
. Suppose now that is a subbasis, which generates the basis for the topology of . If is a basic open set, then
where each . Then
By assumption, each is open, so is their (finite) intersection .
|Title||testing for continuity via basic open sets|
|Date of creation||2013-03-22 19:08:55|
|Last modified on||2013-03-22 19:08:55|
|Last modified by||CWoo (3771)|