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Dimensions, embeddings and iterated function systems
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Margaris, Alexandros (2019) Dimensions, embeddings and iterated function systems. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3492132~S15
Abstract
In this thesis, we study the regularity of embeddings of finite dimensional subsets of Banach spaces into Euclidean spaces. We first consider subsets of Banach spaces with finite box{counting dimension and extend an embedding result due to Hunt & Kaloshin [15], which was previously known only for subsets of Hilbert spaces.
We then focus on almost homogeneous subsets of Banach spaces, which is a weaker notion of homogeneous sets, or sets with finite Assouad dimension. Olson & Robinson [25] showed that if X is a subset of a Hilbert space and X
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Banach spaces., Embeddings (Mathematics), Hilbert space | ||||
Official Date: | July 2019 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Robinson, James C. (James Cooper), 1969- | ||||
Sponsors: | Engineering and Physical Sciences Research Council ; University of Warwick. Department of Mathematics. | ||||
Format of File: | |||||
Extent: | iv, 100 leaves : illustrations | ||||
Language: | eng |
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