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Finite closed coverings of compact quantum spaces

Piotr M. Hajac, Atabey Kaygun, Bartosz Zieliński (2012)

Banach Center Publications

We consider the poset of all non-empty finite subsets of the set of natural numbers, use the poset structure to topologise it with the Alexandrov topology, and call the thus obtained topological space the universal partition space. Then we show that it is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this partition space. In technical terms, we prove that the category of finitely supported...

Finitely generated almost universal varieties of 0 -lattices

Václav Koubek, Jiří Sichler (2005)

Commentationes Mathematicae Universitatis Carolinae

A concrete category 𝕂 is (algebraically) universal if any category of algebras has a full embedding into 𝕂 , and 𝕂 is almost universal if there is a class 𝒞 of 𝕂 -objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of 0 -lattices which are almost universal.

Fixed points with respect to the L-slice homomorphism σ a

K.S. Sabna, N.R. Mangalambal (2019)

Archivum Mathematicum

Given a locale L and a join semilattice J with bottom element 0 J , a new concept ( σ , J ) called L -slice is defined,where σ is as an action of the locale L on the join semilattice J . The L -slice ( σ , J ) adopts topological properties of the locale L through the action σ . It is shown that for each a L , σ a is an interior operator on ( σ , J ) .The collection M = { σ a ; a L } is a Priestly space and a subslice of L - Hom ( J , J ) . If the locale L is spatial we establish an isomorphism between the L -slices ( σ , L ) and ( δ , M ) . We have shown that the fixed set of σ a ,...

Folding theory applied to BL-algebras

Young Jun, Jung Ko (2004)

Open Mathematics

The notion of n-fold grisly deductive systems is introduced. Some conditions for a deductive system to be an n-fold grisly deductive system are provided. Extension property for n-fold grisly deductive system is established.

Formalization of Generalized Almost Distributive Lattices

Adam Grabowski (2014)

Formalized Mathematics

Almost Distributive Lattices (ADL) are structures defined by Swamy and Rao [14] as a common abstraction of some generalizations of the Boolean algebra. In our paper, we deal with a certain further generalization of ADLs, namely the Generalized Almost Distributive Lattices (GADL). Our main aim was to give the formal counterpart of this structure and we succeeded formalizing all items from the Section 3 of Rao et al.’s paper [13]. Essentially among GADLs we can find structures which are neither V-commutative...

Frame monomorphisms and a feature of the l -group of Baire functions on a topological space

Richard N. Ball, Anthony W. Hager (2013)

Commentationes Mathematicae Universitatis Carolinae

“The kernel functor” W k LFrm from the category W of archimedean lattice-ordered groups with distinguished weak unit onto LFrm, of Lindelöf completely regular frames, preserves and reflects monics. In W , monics are one-to-one, but not necessarily so in LFrm. An embedding ϕ W for which k ϕ is one-to-one is termed kernel-injective, or KI; these are the topic of this paper. The situation is contrasted with kernel-surjective and -preserving (KS and KP). The W -objects every embedding of which is KI are characterized;...

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