In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...

In this paper we introduce a notion of vertex Lie algebra U , in a way a “half” of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U). We show that we may consider U as a subset U ⊂ V(U) which generates V(U) and that the vertex Lie algebra structure on U is induced by the vertex algebra structure on V(U). Moreover, for any vertex ...

We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms. The picture is rather different. Our main results are partial characterisations of countable graphs and posets with this property; an analogue of Fraı̈ssé’s Theorem; and representations of monoids as endomorphism monoids of such structures. ∗This...

This paper introduces accumulation into list homomorphisms for systematic development of both efficient and correct parallel programs. New parallelizable recursive pattern called H-homomorphism is given, and transformations from sequential patterns in the H-form and Hform into (H-)homomorphism are shown. We illustrate the power of our formalization by developing a novel and general parallel pro...

We discuss the construction of a long semi-exact Mayer–Vietoris sequence for homology any finite union open subspaces. This is used to obtain topological conditions representation integral meromorphic n-form on an n-dimensional complex manifold in terms Grothendieck residues. For such exist, it necessary that cycle integration separates set polar hypersurfaces form. The separation condition num...