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    • 03) Bitlis Eren Üniversitesi Fen Bilimleri Dergisi
    • Cilt 07, Sayı 1 (2018)
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    • 03) Bitlis Eren Üniversitesi Fen Bilimleri Dergisi
    • Cilt 07, Sayı 1 (2018)
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    Some Theorems on Compactness and Completeness

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    Date
    2018
    Author
    KAYA, Ufuk
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    Abstract
    In this work, we prove the validity of the converses of some theorems about compactness and completeness. After we give some required basic definitions and theorems, we define monolimit property for sequences and nets, convergent subsequences property for first countable Hausdorff space, convergent subnets property for general Hausdorff space, and also, we show that those properties are equivalent to compactness and sequential compactness. On the other hand, we prove that a metric space is complete iff every totally bounded subset of it is relatively compact. Finally, we give some examples from some abstract spaces and normed spaces for application.
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    http://dspace.beu.edu.tr:8080/xmlui/handle/123456789/14168
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    • Cilt 07, Sayı 1 (2018) [21]





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