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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| Language: | en |
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University of Canterbury. Mathematics and Statistics
2008
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| Online Access: | http://hdl.handle.net/10092/1823 |
| Summary: | 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. |
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