Browsing by Author "Salbany, Sergio de Ornelas"

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    Compactifications, subordinations and uniformities
    (1968) Salbany, Sergio de Ornelas; Schlagbauer, H
    This thesis relates hausdorff compactifications of spaces and other structures on the space. Each chapter starts with an introduction, which describes its content, and ends with a collection of notes, where the references relevant to the chapter are given. Most of the thesis is self-contained. The standard reference throughout is: General Topology, by Kelley. The notation is as in Kelley. We often use the abbreviations - s. t. for such that; iff for if and only if; i.e. for that is. This thesis arose from an attempt to prove the essential steps in the construction of vX, described by Aleksandrov in his survey Some Results in the Theory of Topological Spaces, Obtained Within the Last Twenty-Five Years.
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    Metrization of ordered topological spaces
    (1974) Colquhoun, Alan; Salbany, Sergio de Ornelas
    In 1969, Lutzer proved that a linearly ordered topological space with a Gδ-diagonal is metrizable. This appears to be the first work in the field of metrization of ordered topological spaces. Very little seems to have been done in this direction. This thesis is a study of the various conditions necessary for metrizability of such spaces. One of the earliest papers concerned with ordered topological spaces is that of Eilenberg. Since then, ordered spaces have been considered by various authors, but few considered the conditions under which such spaces would be metrizable. Bennet gave a characterization of metrizability for a linearly ordered topological space with a σ-point finite base. A linearly ordered topological space is a space for which the interval topology coincides with the original topology for the space. We investigate the metrizability of linearly ordered topological space satisfying certain covering properties, countability conditions on the base, certain conditions on the diagonal and spaces which admit a symmetric. We obtain four characterizations of metrizability for linearly ordered topological space in terms of some of the above notions.
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    On coincidence of algebras of functions with C(X)
    (1973) Sager, Jürgen; Kotzé, W; Salbany, Sergio de Ornelas
    The study of approximation of continuous functions has always evoked great interest. The classical result in the theory of approximation is Weierstrass's theorem on the uniform approximation of continuous functions on a bounded closed interval by polynomials. This result was later extended to compact Hausdorff topological spaces by M. H. Stone. Approximation theorems were later also established for almost compact spaces by Hewitt, and for Lindelöf and almost Lindelöf spaces by Hager and Frolik. All the results above were originally proved for real-valued functions. Indeed, they do not generally extend to complex-valued functions; one has to consider different types of algebras and employ different techniques. The theory of complex measures plays an important part in this case. In this thesis we discuss approximation theorems of the Stone-Weierstrass type. We found it convenient to divide the thesis into two parts. Part I concerns real-valued runctions and Part II dicusses the complex case. At the end of each part we have included short bibliographical notes.