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On Acyclicity Properties of Complements of Subsets in the Hilbert Cube
Başlık:
On Acyclicity Properties of Complements of Subsets in the Hilbert Cube
Yazar:
Amarasinghe, Ashwini K., author.
ISBN:
9780438120259
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (45 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Özet:
The first part of this dissertation is on extending a non-separation theorem for the complement of finite dimensional subspace of the space of complete non-negatively curved metrics on the plane by Belagradek and Hu. We generalize their result to complements of weakly infinite dimensional (WID) compacta. An extension for a similar non-separation theorem by Belagradek and Hu for the moduli space is then obtained for spaces having Haver's property-C. It is still an open question whether every weakly infinite dimensional compact metric space have property-C..
In the second part of this dissertation we answer a question by Banach, Zarichnyi and Kauty regarding the acyclicity of the complement of closed WID subspaces of a Hilbert Cube affirmatively. In the process, we define cohomologically strongly infinite-dimensional (CSID) compacta with respect to any ring. A space that is not CSID is called cohomologically weakly infinite dimensional (CWID). We prove that the complement of any CWID compactum in the Hilbert cube is acyclic with respect to any ring. Consequently, it is shown that the class of strongly infinite-dimensional compacta is properly contains the class of CSID compacta, and it is further shown that being CWID is hereditary with respect to closed subsets.
The third part of this dissertation is about extending the above results to sigma-compacta in the Hilbert Cube. We first prove that removing a closed WID subspace does not change the homology type of a Hilbert cube manifold, and then we prove the main result, that states the complement of a sigma-compactum in the Hilbert Cube is Steenrod acyclic in the dimension 0.
Notlar:
School code: 0070
Konu Başlığı:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(696567.1) | 696567-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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