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Domain representability of C p ( X )

Harold Bennett, David Lutzer (2008)

Fundamenta Mathematicae

Let C p ( X ) 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) C p ( X ) is Scott-domain representable; (b) C p ( X ) 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 C p ( X ) is...

Domain-representable spaces

Harold Bennett, David Lutzer (2006)

Fundamenta Mathematicae

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 G δ -subspace of X. It follows that any Čech-complete...

Dominating analytic families

Anastasis Kamburelis (1998)

Fundamenta Mathematicae

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.

Domination properties in ordered Banach algebras

H. du T. Mouton, S. Mouton (2002)

Studia Mathematica

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....

Doubly stochastic matrices and the Bruhat order

Richard A. Brualdi, Geir Dahl, Eliseu Fritscher (2016)

Czechoslovak Mathematical Journal

The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order n 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 Ω n of doubly stochastic matrices (convex hull of n × n permutation matrices). An alternative description of this partial order is given. We define a class of special faces of Ω n induced by permutation matrices,...

Dual commutative hyper K-ideals of type 1 in hyper K-algebras of order 3.

L. Torkzadeh, M. M. Zahedi (2006)

Mathware and Soft Computing

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.

Duality for CCD lattices.

Marmolejo, Francisco, Rosebrugh, Robert, Wood, R.J. (2009)

Theory and Applications of Categories [electronic only]

Duality for Hilbert algebras with supremum: An application

Hernando Gaitan (2017)

Mathematica Bohemica

We modify slightly the definition of H -partial functions given by Celani and Montangie (2012); these partial functions are the morphisms in the category of H ∨ -space and this category is the dual category of the category with objects the Hilbert algebras with supremum and morphisms, the algebraic homomorphisms. As an application we show that finite pure Hilbert algebras with supremum are determined by the monoid of their endomorphisms.

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