Compactness Under Constructive Scrutiny
The aim of this thesis is to understand the constructive scope of compactness. We show that it is possible to define, constructively, a meaningful notion of compactness in a more general setting than the uniform/metric space one. Furthermore, we show that it is not possible to define compactness cons...
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University of Canterbury. Mathematics and Statistics
2008
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| Online Access: | http://hdl.handle.net/10092/1823 |
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ndltd-canterbury.ac.nz-oai-ir.canterbury.ac.nz-10092-1823 |
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ndltd-canterbury.ac.nz-oai-ir.canterbury.ac.nz-10092-18232015-03-30T15:29:00ZCompactness Under Constructive ScrutinyDiener, HannesThe aim of this thesis is to understand the constructive scope of compactness. We show that it is possible to define, constructively, a meaningful notion of compactness in a more general setting than the uniform/metric space one. Furthermore, we show that it is not possible to define compactness constructively in a topological space. We investigate exactly what principles are necessary and sufficient to prove classically true theorems about compactness, as well as their antitheses. We develop beginnings of a constructive theory of differentiable manifolds.University of Canterbury. Mathematics and Statistics2008-11-20T20:07:36Z2008-11-20T20:07:36Z2008Electronic thesis or dissertationTexthttp://hdl.handle.net/10092/1823enNZCUCopyright Hannes Dienerhttp://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
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NDLTD |
| language |
en |
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NDLTD |
| description |
The aim of this thesis is to understand the constructive scope of compactness.
We show that it is possible to define, constructively, a meaningful notion of compactness in a more general setting than the uniform/metric space one. Furthermore, we show that it is not possible to define compactness constructively in a topological space.
We investigate exactly what principles are necessary and sufficient to prove classically true theorems about compactness, as well as their antitheses.
We develop beginnings of a constructive theory of differentiable manifolds. |
| author |
Diener, Hannes |
| spellingShingle |
Diener, Hannes Compactness Under Constructive Scrutiny |
| author_facet |
Diener, Hannes |
| author_sort |
Diener, Hannes |
| title |
Compactness Under Constructive Scrutiny |
| title_short |
Compactness Under Constructive Scrutiny |
| title_full |
Compactness Under Constructive Scrutiny |
| title_fullStr |
Compactness Under Constructive Scrutiny |
| title_full_unstemmed |
Compactness Under Constructive Scrutiny |
| title_sort |
compactness under constructive scrutiny |
| publisher |
University of Canterbury. Mathematics and Statistics |
| publishDate |
2008 |
| url |
http://hdl.handle.net/10092/1823 |
| work_keys_str_mv |
AT dienerhannes compactnessunderconstructivescrutiny |
| _version_ |
1716798462214799360 |