The Lattice of Compactifications of a Locally Compact Space
Issue Date
2016-05-31Author
Eichelberger, Luke Alan
Publisher
University of Kansas
Format
53 pages
Type
Thesis
Degree Level
M.A.
Discipline
Mathematics
Rights
Copyright held by the author.
Metadata
Show full item recordAbstract
This is an expanded version of [5] by Magill. The results of [5] are proven with greater detail and any result stated in [5] but not proven is proven here. Let K (X) and K (Y) be used to indicate the lattice of Hausdorff compactifications of locally compact, non-compact spaces X and Y with X and Y Tychonoff. This paper primarily concerns how a lattice isomorphism between K (X) and K (Y) exists if and only if a homeomorphism between particular extensions of X and Y exists with specified properties. On the way to proving the main results, we prove several lemmas about β − families of compact extensions of Tychonoff spaces. Some of the Lemmas slightly generalize corresponding lemmas in [5]. Efforts are made to make this paper self- contained.
Collections
- Mathematics Dissertations and Theses [113]
- Theses [3710]
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