proof of Lindelöf theorem
Let be a second countable topological space, any subset and an open cover of . Let be a countable basis for ; then is a countable basis of the subspace topology on A. Then for each there is some with , and so there is such that .
Then is a countable open cover of . For each , choose such that . Then is a countable subcover of from .
|Title||proof of Lindelöf theorem|
|Date of creation||2013-03-22 12:56:31|
|Last modified on||2013-03-22 12:56:31|
|Last modified by||Evandar (27)|