1. The Baire category theorem - Aarhus Universitet

More documents

Recommendations

Info

Proof of Baire’s category theorem - continued The proof is now completed as follows; first the case when S is a locally compact Hausdorff space: B0 ⊇ B1 ⊇ B2 ⊇ B3 ⊇ ... and each Bk,k ≥ 1, is compact and non-empty. It follows that ∞ k=1 Bk = ∅. Since Bk ⊆ Vk−1 for all k, we find that ∞ ∞ Vk. k=1 Bk ⊆ k=0 Klaus Thomsen 1. The Baire category theorem
Proof of Baire’s category theorem - continued The proof is now completed as follows; first the case when S is a locally compact Hausdorff space: B0 ⊇ B1 ⊇ B2 ⊇ B3 ⊇ ... and each Bk,k ≥ 1, is compact and non-empty. It follows that ∞ k=1 Bk = ∅. Since Bk ⊆ Vk−1 for all k, we find that ∞ ∞ Vk. k=1 Bk ⊆ But ∞ k=1 Bk ⊆ B0, so we see that ∞ k=1 Bk ⊆ k=0 ∞ Vk ∩ B0, k=1 which was what we wanted to prove. 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:
Page 25 and 26:
Page 27 and 28: 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 77: 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?