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Hausdorff ’s theorem for posets that satisfy the finite antichain property

Uri Abraham, Robert Bonnet (1999)

Fundamenta Mathematicae

Hausdorff characterized the class of scattered linear orderings as the least family of linear orderings that includes the ordinals and is closed under ordinal summations and inversions. We formulate and prove a corresponding characterization of the class of scattered partial orderings that satisfy the finite antichain condition (FAC).  Consider the least class of partial orderings containing the class of well-founded orderings that satisfy the FAC and is closed under the following operations: (1)...

Hausdorffness in intuitionistic fuzzy topological spaces.

Francisco Gallego Lupiáñez (2003)

Mathware and Soft Computing

The basic concepts of the theory of intuitionistic fuzzy topological spaces have been defined by D. Çoker and co-workers. In this paper, we define new notions of Hausdorffness in the intuitionistic fuzzy sense, and obtain some new properties, in particular on convergence.

Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations

Boaz Tsaban, Lubomyr Zdomsky (2012)

Journal of the European Mathematical Society

A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii α 1 spaces, for which every sheaf at a point can be amalgamated in a natural way. Let C p ( X ) denote the space of continuous real-valued functions on X with the topology of pointwise convergence. Our main result...

Hierarchies of function classes defined by the first-value operator

Armin Hemmerling (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The first-value operator assigns to any sequence of partial functions of the same type a new such function. Its domain is the union of the domains of the sequence functions, and its value at any point is just the value of the first function in the sequence which is defined at that point. In this paper, the first-value operator is applied to establish hierarchies of classes of functions under various settings. For effective sequences of computable discrete functions, we obtain a hierarchy connected...

Hierarchies of function classes defined by the first-value operator

Armin Hemmerling (2007)

RAIRO - Theoretical Informatics and Applications

The first-value operator assigns to any sequence of partial functions of the same type a new such function. Its domain is the union of the domains of the sequence functions, and its value at any point is just the value of the first function in the sequence which is defined at that point. In this paper, the first-value operator is applied to establish hierarchies of classes of functions under various settings. For effective sequences of computable discrete functions, we obtain a hierarchy connected...

Historic forcing for Depth

Andrzej Rosłanowski, Saharon Shelah (2001)

Colloquium Mathematicae

We show that, consistently, for some regular cardinals θ <λ, there exists a Boolean algebra 𝔹 such that |𝔹| = λ⁺ and for every subalgebra 𝔹'⊆ 𝔹 of size λ⁺ we have Depth(𝔹') = θ.

HOD-supercompactness, Indestructibility, and Level by Level Equivalence

Arthur W. Apter, Shoshana Friedman (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

In an attempt to extend the property of being supercompact but not HOD-supercompact to a proper class of indestructibly supercompact cardinals, a theorem is discovered about a proper class of indestructibly supercompact cardinals which reveals a surprising incompatibility. However, it is still possible to force to get a model in which the property of being supercompact but not HOD-supercompact holds for the least supercompact cardinal κ₀, κ₀ is indestructibly supercompact, the strongly compact and...

Homogeneous aggregation operators

Tatiana Rückschlossová, Roman Rückschloss (2006)

Kybernetika

Recently, the utilization of invariant aggregation operators, i.e., aggregation operators not depending on a given scale of measurement was found as a very current theme. One type of invariantness of aggregation operators is the homogeneity what means that an aggregation operator is invariant with respect to multiplication by a constant. We present here a complete characterization of homogeneous aggregation operators. We discuss a relationship between homogeneity, kernel property and shift-invariance...

Homology theory in the alternative set theory I. Algebraic preliminaries

Jaroslav Guričan (1991)

Commentationes Mathematicae Universitatis Carolinae

The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative π -group), is introduced. Commutative π -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...

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