Order compactifications of totally ordered topological spaces
نویسندگان
چکیده
منابع مشابه
Order-Compactifications of Totally Ordered Spaces: Revisited
Order-compactifications of totally ordered spaces were described by Blatter (J Approx Theory 13:56–65, 1975) and by Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Their results generalize a similar characterization of order-compactifications of linearly ordered spaces, obtained independently by Fedorčuk (Soviet Math Dokl 7:1011–1014, 1966; Sib Math J 10:124–132, 1969) and Kaufman (Col...
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We describe the semilattice of ordered compactifications ofX×Y smaller than βoX×βoY whereX and Y are certain totally ordered topological spaces, and where βoZ denotes the Stone–Čech orderedor Nachbin-compactification of Z. These basic cases are used to illustrate techniques for describing the semilattice of ordered compactifications ofX×Y smaller than βoX×βoY for arbitrary totally ordered topol...
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Salbany, S. and T. Todorov, Nonstandard and standard cornpactifications of ordered topological spaces, Topology and its Applications 47 (1992) 35-52. We construct the Nachbin ordered compactification and the ordered realcornpactification, a notion defined in the paper, of a given ordered topological space as nonstandard ordered hulls. The maximal ideals in the algebras of the differences of mon...
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The lattice of ordered compactifications of a topological sum of a finite number of totally ordered spaces is investigated. This investigation proceeds by decomposing the lattice into equivalence classes determined by the identification of essential pairs of singularities. This lattice of equivalence classes is isomorphic to a power set lattice. Each of these equivalence classes is further deco...
متن کاملLinearly Ordered Topological Spaces
This work is devoted to the study of certain cardinality modifications of paracompactness and compactness in the setting of linearly ordered spaces. Some of the concepts treated here have previously been studied by Aquaro [l]1, Gulden [4], Kennison [5], Mansfield [6], Morita [7], and Poppe [9]. On the other hand, the concept of m-boundedness, introduced in §2, is new. Our main results (Theorems...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1975
ISSN: 0021-9045
DOI: 10.1016/0021-9045(75)90014-3