1,720,962 research outputs found
Operations that preserve integrability, and truncated Riesz spaces
Get PDFFor any real number , we characterise the operations
that preserve -integrability, i.e., the
operations under which, for every measure , the set
is closed. We investigate the infinitary variety of algebras whose operations
are exactly such functions. It turns out that this variety coincides with the
category of Dedekind -complete truncated Riesz spaces, where truncation
is meant in the sense of R. N. Ball. We also prove that generates
this variety. From this, we exhibit a concrete model of the free Dedekind
-complete truncated Riesz spaces. Analogous results are obtained for
operations that preserve -integrability over finite measure spaces: the
corresponding variety is shown to coincide with the much studied category of
Dedekind -complete Riesz spaces with weak unit, is proved
to generate this variety, and a concrete model of the free Dedekind
-complete Riesz spaces with weak unit is exhibited.Comment: Changed the definition of "conditionally partitionable measure
space", results unchanged; minor change
Dedekind σ-complete l-groups and Riesz spaces as varieties
No full textWe prove that the category of Dedekind σ-complete Riesz spaces is an infinitary variety, and we provide an explicit equational axiomatization. In fact, we show that finitely many axioms suffice over the usual equational axiomatization of Riesz spaces. Our main result is that R, regarded as a Dedekind σ-complete Riesz space, generates this category as a variety; further, we use this fact to obtain the even stronger result that R generates this category as a quasi-variety. Analogous results are established for the categories of (i) Dedekind σ-complete Riesz spaces with a weak order unit, (ii) Dedekind σ-complete lattice-ordered groups, and (iii) Dedekind σ-complete lattice-ordered groups with a weak order unit
The dual of compact ordered spaces is a variety
Get PDFIn a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the
dual of the category of compact partially ordered spaces and monotone
continuous maps is a quasi-variety - not finitary, but bounded by .
An open question was: is it also a variety? We show that the answer is
affirmative. We describe the variety by means of a set of finitary operations,
together with an operation of countably infinite arity, and equational axioms.
The dual equivalence is induced by the dualizing object [0,1]
Are locally finite MV-algebras a variety?
No full textWe answer Mundici's problem number 3 (Mundici (2011) [37]): Is the category of locally finite MV-algebras equivalent to an equational class? We prove: 1. The category of locally finite MV-algebras is not equivalent to any finitary variety. 2. More is true: the category of locally finite MV-algebras is not equivalent to any finitely-sorted finitary quasi-variety. 3. The category of locally finite MV-algebras is equivalent to an infinitary variety; with operations of at most countable arity. 4. The category of locally finite MV-algebras is equivalent to a countably-sorted finitary variety. Our proofs rest upon the duality between locally finite MV-algebras and the category of “multisets” by R. Cignoli, E.J. Dubuc and D. Mundici, and known categorical characterisations of varieties and quasi-varieties. In fact, no knowledge of MV-algebras is needed, apart from the aforementioned duality
Equivalence \`a la Mundici for commutative lattice-ordered monoids
Get PDFWe provide a generalization of Mundici's equivalence between unital Abelian
lattice-ordered groups and MV-algebras: the category of unital commutative
lattice-ordered groups is equivalent to the category of MV-monoidal algebras.
Roughly speaking, the structures we call unital commutative lattice-ordered
groups are unital Abelian lattice-ordered groups without the unary operation . The primitive operations are , , , , , .
A prime example of these structures is , with the obvious
interpretation of the operations. Analogously, MV-monoidal algebras are
MV-algebras without the negation . The primitive operations
are , , , , , . A motivating example of
MV-monoidal algebra is the negation-free reduct of the standard MV-algebra . We obtain the original Mundici's equivalence as a
corollary of our main result
On the Axiomatisability of the Dual of Compact Ordered Spaces
Get PDFWe provide a direct and elementary proof of the fact that the category of Nachbin's compact ordered spaces is dually equivalent to an N-1-ary variety of algebras. Further, we show that N-1 is a sharp bound: compact ordered spaces are not dually equivalent to any SP-class of finitary algebras
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
IMMUNOCYTOCHEMICAL DISTRIBUTION OF EXTRACELLULAR-MATRIX RECEPTORS IN HUMAN OSTEOCLASTS - A BETA-3 INTEGRIN IS COLOCALIZED WITH VINCULIN AND TALIN IN THE PODOSOMES OF OSTEOCLASTOMA GIANT-CELLS
No full textImmunocytochemical distribution of extracellular matrix receptors in human osteoclasts. A β3 integrin is colocalized with vinculin and talin in the podosomes of osteoclastoma giant cells
No full text- …
