8,009 research outputs found
First Baire class functions in the pluri-fine topology
Let be the first Baire class of real functions in
the pluri-fine topology on an open set and let
be the first functional Lebesgue class of real
functions in the same topology. We prove the equality and show that for every there is a separately continuous function in the pluri-fine topology on such that is the diagonal of
Comment: 10 page
A Categorical View on Algebraic Lattices in Formal Concept Analysis
Formal concept analysis has grown from a new branch of the mathematical field
of lattice theory to a widely recognized tool in Computer Science and
elsewhere. In order to fully benefit from this theory, we believe that it can
be enriched with notions such as approximation by computation or
representability. The latter are commonly studied in denotational semantics and
domain theory and captured most prominently by the notion of algebraicity, e.g.
of lattices. In this paper, we explore the notion of algebraicity in formal
concept analysis from a category-theoretical perspective. To this end, we build
on the the notion of approximable concept with a suitable category and show
that the latter is equivalent to the category of algebraic lattices. At the
same time, the paper provides a relatively comprehensive account of the
representation theory of algebraic lattices in the framework of Stone duality,
relating well-known structures such as Scott information systems with further
formalisms from logic, topology, domains and lattice theory.Comment: 36 page
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