194 research outputs found
Solid weak BCC-algebras
We characterize weak BCC-algebras in which the identity is
satisfied only in the case when elements belong to the same branch
New generalizations of BCI, BCK and Hilbert algebras
We introduce more generalizations of BCI, BCK and of Hilbert algebras, with
proper examples, and show the hierarchies existing between all these algebras,
old and new ones. Namely, we found thirty one new generalizations of BCI and
BCK algebras and twenty generalizations of Hilbert algebras.Comment: Open problems 11.3 (1), (2), (3) were solved. New (20'), (21''),
Theorems 2.4,2.6, Cor. 2.5, 5.5 adde
Tubular configurations: equivariant scanning and splitting
Replacing configurations of points by configurations of tubular
neighbourhoods (or discs) in a manifold, we are able to define a natural
scanning map that is equivariant under the action of the diffeomorphism group
of the manifold. We also construct the so-called power set map of configuration
spaces diffeomorphism equivariantly. Combining these two constructions yields
stable splittings in the sense of Snaith and generalisations thereof that are
equivariant. In particular one deduces stable splittings of homotopy orbit
spaces. As an application the homology injectivity is proved for diffeomorphism
of manifolds that fix an increasing number of points. Throughout we work with
configurations spaces with labels in a fibre bundle.Comment: 24 page
On branchwise commutative pseudo-BCH algebras
Basic properties of branches of pseudo-BCH algebras are described. Next, the concept of a branchwise commutative pseudo-BCH algebra is introduced. Some conditions equivalent to branchwise commutativity are given. It is proved that every branchwise commutative pseudo-BCH algebra is a pseudo-BCI algebra
- …