We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors. The first known result of this kind, a consequence of a theorem by A. H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many...

In this paper we define simulations up-to a preorder and show how we can use them to provide a coinductive, simulation-like, characterization of semantic preorders for processes. The result applies to a wide class of preorders, in particular to all semantic preorders coarser than the ready simulation preorder in the linear time-branching time spectrum. An interesting but unexpected result is th...

When using the Curry-Howard correspondence in order to obtain executable programs from mathematical proofs, we are faced with a difficult problem : to interpret each axiom of our axiom system for mathematics (which may be, for example, second order classical logic, or classical set theory) as an instruction of our programming language. This problem has been solved for the axiom of excluded midd...

arabic grammar aimed to protect arabic language from any erroneous pronunciations and writings. but grammar itself came to be complicated and came to be a goal rather than a means of reaching to exact learning of arabic language. some of contemporary arabic linguists strived to simplify the arabic grammar and rid it from any complexities. experts like ibrahim mostafa, makhzumi, showqii dhaif an...