Topologies, continuity and bisimulations
Topologies, Continuity and Bisimulations
The notion of a bisimulation relation is of basic importance in many areas of computation theory and logic. Of late, it has come to take a particular significance in work on the formal analysis and verification of hybrid control systems, where system properties are expressible by formulas of the modal μ-calculus or weaker temporal logics. Our purpose here is to give an analysis of the concept of bisimulation, starting with the observation that the zig-zag conditions are suggestive of some...
Topologies on generalized semi-inner product spaces
Topologies on groups determined by right cancellable ultrafilters
For every discrete group , the Stone-Čech compactification of has a natural structure of a compact right topological semigroup. An ultrafilter , where , is called right cancellable if, given any , implies . For every right cancellable ultrafilter , we denote by the group endowed with the strongest left invariant topology in which converges to the identity of . For any countable group and any right cancellable ultrafilters , we show that is homeomorphic to if and only if...
Topologies On Spaces Of Continuous Multifunctions
Topologies on Spaces of Vector-Valued Continuous Functions. II.
Topologies sur des espaces ordonnés
Topologies uniquely determined by their continuous self maps
Toroidal decompositions of and a family of 3-dimensional ANR’s (AR’s)
Totally discontinuous connectivity functions
Trajectories, first return limiting notions and rings of -connected and iteratively -connected functions
In the paper the existing results concerning a special kind of trajectories and the theory of first return continuous functions connected with them are used to examine some algebraic properties of classes of functions. To that end we define a new class of functions (denoted ) contained between the families (widely described in literature) of Darboux Baire 1 functions () and connectivity functions (). The solutions to our problems are based, among other, on the suitable construction of the ring,...
Transducer, generalized relays and their characterization
Transfer positive hemicontinuity and zeros, coincidences, and fixed points of maps in topological vector spaces.
Transition operator characterizations of compact and maximally almost periodic locally compact groups.
Translation properties of finite partitions of the positive integers
Trivial bundles and near-homeomorphisms
Trivial bundles of spaces of probability measures and countable-dimensionality
The probability measure functor P carries open continuous mappings of compact metric spaces into Q-bundles provided Y is countable-dimensional and all fibers are infinite. This answers a question raised by V. Fedorchuk.
True preimages of compact or separable sets for functional analysts
We discuss various results on the existence of ‘true’ preimages under continuous open maps between -spaces, -lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.
Truncated symmetric products and configuration spaces.
Two criteria thrusting simple connectedness on manifolds