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• W1990186565 abstract "In this paper, the class of all linearly ordered topological spaces (LOTS) quasi-ordered by the embeddability relation is investigated. In ZFC it is proved that for countable LOTS this quasi-order has both a maximal (universal) element and a finite basis. For the class of uncountable LOTS of cardinality $kappa$ it is proved that this quasi-order has no maximal element for $kappa$ at least the size of the continuum and that in fact the dominating number for such quasi-orders is maximal, i.e. $2^kappa$. Certain subclasses of LOTS, such as the separable LOTS, are studied with respect to the top and internal structure of their respective embedding quasi-order. The basis problem for uncountable LOTS is also considered; assuming the Proper Forcing Axiom there is an eleven element basis for the class of uncountable LOTS and a six element basis for the class of dense uncountable LOTS in which all points have countable cofinality and coinitiality." @default.
• W1990186565 created "2016-06-24" @default.
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• W1990186565 date "2011-02-10" @default.
• W1990186565 modified "2023-09-27" @default.
• W1990186565 title "The embedding structure for linearly ordered topological spaces" @default.
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