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Firm complettion in metrically generated construcs with application to function spaces and sobrification

Tuesday, 27 May, 2008 - 16:00
Campus: Brussels Humanities, Sciences & Engineering campus
Faculty: Science and Bio-engineering Sciences
D
2.01
Eva Vandersmissen
phd defence

In this thesis we fully exploit the setting of metrically generated constructs for the study of uniqueness of completion. For a metrically generated construct X, we develop a technique to lift an existing completeness notion in an auxiliary construct A to a suitable notion of completeness in X and we formulate conditions under which we can build a firm completion theory in the subconstruct X_0 consisting of T_0 objects. Application of this technique to concrete cases results in many interesting completion theories and provides us with a far better understanding of several existing completion theories. An extra feature is that this study allows applications to function spaces and sobrification.