Dimension and decomposition in modular upper-continuous lattices

Abstract In the paper some properties of sets of points of approximate continuity and ϱ-upper continuity are presented. We will show that for every Lebesgue measurable set E ⊂ ℝ there exists a function f : ℝ → ℝ which is approximately (ϱ-upper) continuous exactly at points from E. We also study properties of sets of points at which real function has Denjoy property. Some other related topics are discussed.

Download Full-text

Linear types and approximation

Mathematical Structures in Computer Science ◽

10.1017/s0960129500003200 ◽

2000 ◽

Vol 10 (6) ◽

pp. 719-745 ◽

Cited By ~ 4

Author(s):

MICHAEL HUTH ◽

ACHIM JUNG ◽

KLAUS KEIMEL

Keyword(s):

Full Subcategory ◽

Linear Logic ◽

Domain Theory ◽

Classical Domain ◽

Complete Distributivity ◽

Linear Types ◽

Continuous Lattices

We study continuous lattices with maps that preserve all suprema rather than only directed ones. We introduce the (full) subcategory of FS-lattices, which turns out to be *-autonomous, and in fact maximal with this property. FS-lattices are studied in the presence of distributivity and algebraicity. The theory is extremely rich with numerous connections to classical Domain Theory, complete distributivity, Topology and models of Linear Logic.

Download Full-text

Some operators and dimensions in modular meet-continuous lattices

Journal of Algebra and Its Applications ◽

10.1142/s0219498818500949 ◽

2018 ◽

Vol 17 (05) ◽

pp. 1850094 ◽

Cited By ~ 1

Author(s):

Mauricio Medina Bárcenas ◽

José Ríos Montes ◽

Angel Zaldívar Corichi

Keyword(s):

Complete Lattice ◽

Monotone Function ◽

Continuous Lattice ◽

Continuous Lattices

Given a complete modular meet-continuous lattice [Formula: see text], an inflator on [Formula: see text] is a monotone function [Formula: see text] such that [Formula: see text] for all [Formula: see text]. If [Formula: see text] is the set of all inflators on [Formula: see text], then [Formula: see text] is a complete lattice. Motivated by preradical theory, we introduce two operators, the totalizer and the equalizer. We obtain some properties of these operators and see how they are related to the structure of the lattice [Formula: see text] and with the concept of dimension.

Download Full-text