Browsing by Author "Schauerte, Anneliese"

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    Functorial quasi-uniformities over partially ordered spaces
    (1988) Schauerte, Anneliese; Brümmer, Guillaume C L
    Ordered spaces were introduced by Leopoldo Nachbin [1948 a, b, c, 1950, 1965]. We will be primarily concerned with completely regular ordered spaces, because they are precisely those ordered spaces which admit quasi-uniform structures. A recent and convenient study of these spaces is in the book by P. Fletcher and W.F. Lindgren [1982]. In this thesis we consider functorial quasi-uniformities over (partially) ordered spaces. The functorial methods which we use were developed by Brummer [1971, 1977, 1979, 1982] and Brummer and Hager [1984, 1987] in the context of functorial uniformities over completely regular topological spaces, and of functorial quasi-uniformities over pairwise. completely regular bitopological spaces. We obtain results which are to a large extent analogous to results in those papers. We also introduce some functors which relate our functorial quasi-uniformities to the structures studied by Brummer and others (e.g. Salbany [1984]).
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    Local connectedness of frames
    (2004) Mushaandja, Zechariah; Schauerte, Anneliese
    In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new term for one of them. We also prove that, using Baboolal's methods, if the Stone-Cech compactification βL is locally connected then L need not be locally connected for completely regular frame L. This happens in chapter 5.
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    Strict extensions in pointfree topology
    (2013) Apfel, Gayle Renay; Schauerte, Anneliese; Künzi, Hans-Peter A
    Extensions of spaces have been constructed and used since the 19th century, for example, to form the complex sphere from the complex plane by adding a point at in nity. Once topological spaces were invented in the 20th century, completions and compactications became important examples of extensions. Banaschewski wrote that extension problems have a """"philosophical charm"""" in that they seem to ask the question: """"What possibilities in the unknown are determined by the known?"""" Strict extensions were first defined for topological spaces by Stone. The idea was initially translated into the pointfree setting by Hong, and has since been extensively studied. Just recently, interest has been shown in studying strict extensions in the asymmetric setting of biframes, for example, by Frith and Schauerte. The intention of this dissertation is to provide a systematic and detailed exposition of strict extensions of frames and nearness frames, which can be used as a reference on this topic. For instance, someone interested in pursuing strict extensions of biframes might obtain the relevant background from reading this text, although the topic of strict extensions of biframes itself will not be discussed here.