1. The Baire category theorem - Aarhus Universitet

More documents

Recommendations

Info

Proof of Baire’s category theorem - continued Next we find an open set B2 such that B2 ⊆ V2 ∩ B1 such that d(y,x) ≤ 1 2 when S is complete metric space and such that B2 is compact when S is a locally compact Hausdorff space. This is done as above: Since V2 is dense, V2 ∩ B1 is not empty. Repeat then the previous arguments. Klaus Thomsen 1. The Baire category theorem
Proof of Baire’s category theorem - continued Next we find an open set B2 such that B2 ⊆ V2 ∩ B1 such that d(y,x) ≤ 1 2 when S is complete metric space and such that B2 is compact when S is a locally compact Hausdorff space. This is done as above: Since V2 is dense, V2 ∩ B1 is not empty. Repeat then the previous arguments. Thus we construct recursively a sequence B0,B1,B2,... of open sets such that Bn ⊆ Vn ∩ Bn−1 for all n ≥ 1, d(x,y) ≤ 1 n when x,y ∈ Bn in the case where S is a complete metric space, and such that Bn is compact in the case where S is a locally compact Hausdorff space. Klaus Thomsen 1. The Baire category theorem
Page 1 and 2:
1. The Baire category theorem Klaus
Page 3 and 4:
We read in W. Rudin: Functional Ana
Page 5 and 6:
Definition of first and second cate
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
A subset A of S is nowhere dense wh
Page 13 and 14:
A subset A of S is nowhere dense wh
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Basic properties the notions of cat
Page 23 and 24: Basic properties the notions of cat
Page 33 and 34: The Baire’s category theorem The
Page 35 and 36: Proof of the corollary Reminder ?:
Page 41 and 42: Proof of Baire’s category theorem
Page 47 and 48: On locally compact Hausdorff spaces
Page 73: Proof of Baire’s category theorem
Page 89: Proof of Baire’s category theorem
show all

1. The Baire category theorem - Aarhus Universitet

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?