We study solvability of equations of the form in the groups of order automorphisms of archimedean-complete totally ordered groups of rank 2. We determine exactly which automorphisms of the unique abelian such group have square roots, and we describe all automorphisms of the general ones.
It is shown that divisible effect algebras are in one-to-one correspondence with unit intervals in partially ordered rational vector spaces.
Gli insiemi parziali sono coppie di sottoinsiemi di , dove . Gli insiemi parziali su costituiscono una DMF-algebra, ossia un'algebra di De Morgan in cui la negazione ha un solo punto fisso. Dimostriamo che ogni DMF-algebra è isomorfa a un campo di insiemi parziali. Utilizzando gli insiemi parziali su come aperti, introduciamo il concetto di spazio topologico parziale su . Infine associamo ad ogni DMF-algebra uno spazio topologico parziale i cui clopen compatti costituiscono un campo d'insiemi...
Duffus wrote in his 1978 Ph.D. thesis, “It is not obvious that is connected and imply that is connected”, where and are finite nonempty posets. We show that, indeed, under these hypotheses is connected and .
Let be the space of continuous real-valued functions on X, with the topology of pointwise convergence. We consider the following three properties of a space X: (a) is Scott-domain representable; (b) is domain representable; (c) X is discrete. We show that those three properties are mutually equivalent in any normal T₁-space, and that properties (a) and (c) are equivalent in any completely regular pseudo-normal space. For normal spaces, this generalizes the recent result of Tkachuk that is...
We study domain-representable spaces, i.e., spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order (= domain) with the Scott topology. We show that the Michael and Sorgenfrey lines are of this type, as is any subspace of any space of ordinals. We show that any completely regular space is a closed subset of some domain-representable space, and that if X is domain-representable, then so is any -subspace of X. It follows that any Čech-complete...
Let A be an analytic family of sequences of sets of integers. We show that either A is dominated or it contains a continuum of almost disjoint sequences. From this we obtain a theorem by Shelah that a Suslin c.c.c. forcing adds a Cohen real if it adds an unbounded real.
We recall from [9] the definition and properties of an algebra cone C of a real or complex Banach algebra A. It can be shown that C induces on A an ordering which is compatible with the algebraic structure of A. The Banach algebra A is then called an ordered Banach algebra. An important property that the algebra cone C may have is that of normality. If C is normal, then the order structure and the topology of A are reconciled in a certain way. Ordered Banach algebras have interesting spectral properties....
The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class of doubly stochastic matrices (convex hull of permutation matrices). An alternative description of this partial order is given. We define a class of special faces of induced by permutation matrices,...
In this note we classify the bounded hyper K-algebras of order 3, which have D1 = {1}, D2 = {1,2} and D3 = {0,1} as a dual commutative hyper K-ideal of type 1. In this regard we show that there are such non-isomorphic bounded hyper K-algebras.