We prove some new characterizations of strongly continuous lattices using two new intrinsic topologies and a class of convergences. Lastly we show that the category of strongly continuous lattices and Scott continuous mappings is cartesian closed.
The aim of the present paper is to study the dynamics of a class of
orbitally continuous non-linear mappings defined on the set of real numbers
and to apply the results on dynamics of functions to obtain tests of
divisibility. We show that this class of mappings contains chaotic mappings.
We also draw Julia sets of certain iterations related to multiple lowering
mappings and employ the variations in the complexity of Julia sets to
illustrate the results on the quotient and remainder. The notion of orbital
continuity was introduced by Lj. B. Ciric and is an important tool in
establishing existence of fixed points.
Abstract
New families of uniformities are introduced on
UC(X,Y)
, the class of uniformly continuous mappings between X and Y, where
(X,{\mathcal{U}})
and
(Y,{\mathcal{V}})
are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible.
AbstractWe prove a fixed point theorem for continuous mappings which satisfy a compression-expansion condition on the boundary of a N-dimensional cell of ℝ
For a usual commutative quantale Q (does not necessarily have a unit), we propose a definition of Q-ordered sets by introducing a kind of self-adaptive self-reflexivity. We study their completeness and the related Q-modules of complete lattices. The main result is that, the complete Q-ordered sets and the Q-modules of complete lattices are categorical isomorphic.
Some New Intrinsic Topologies on Complete Lattices and the Cartesian Closedness of the Category of Strongly Continuous Lattices
