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We describe the semilattice of ordered compactifications of X × Y smaller than βoX × βoY where X and Y are certain totally ordered topological spaces, and where βoZ denotes the Stone–Čech ordered- or Nachbin-compactification of Z. These basic cases are used to illustrate techniques for describing the semilattice of ordered compactifications of X × Y smaller than βoX × βoY for arbitrary totally...
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 decomposed...
H-closed extensions of Hausdorff spaces have been studied extensively as a generalization of compactifications of Tychonoff spaces. The collection of H-closed extensions of a space is known to have an upper semilattice structure. Little work has been done to characterize spaces whose collections of H-closed extensions have specified upper semilattice structures. In 1970 J.R. Porter found necessary...
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