On the Order Hereditary Closure Preserving Sum Theorem

A Theorem on Partially Ordered Sets of Order-preserving Mappings

Let P be a partially ordered set and let Pp denote the set of all order-preserving mappings of P to P ordered by/ < g in Pp iif(p) < g(p) for all p £ P. We prove that if P and Q are finite, connected partially ordered sets and Pp = Q<¡ then Psg. Is a partially ordered set determined by its order-preserving mappings? L. M. Gluskin [4] has shown that the set of order-preserving mappings of a part...

On subordination-preserving theorem

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t Let H denote the class of analytic functions in the unit disc on the complex plane C. If the operator I : H ...

Notes on the sum product theorem

On Plain and Hereditary History-Preserving Bisimulation

We investigate the difference between two well-known notions of independence bisimilarity, history-preserving bisimulation and hereditary history-preserving bisimulation. We characterise the difference between the two bisimulations in trace-theoretical terms, advocating the view that the first is (just) a bisimulation for causality, while the second is a bisimulation for concurrency. We explore...

On the Closure of the Sum of Closed Subspaces

We give necessary and sufficient conditions for the sum of closed subspaces of a Hilbert space to be closed. Specifically, we show that the sum will be closed if and only if the angle between the subspaces is not zero, or if and only if the projection of either space into the orthogonal complement of the other is closed. We also give sufficient conditions for the sum to be closed in terms of th...