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Quasicontinuous functions, domains, and extended calculus

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Quasicontinuous functions, domains, and extended calculus

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dc.contributor.author Cazacu, Rodica es_ES
dc.contributor.author Lawson, Jimmie D. es_ES
dc.date.accessioned 2017-06-16T10:40:33Z
dc.date.available 2017-06-16T10:40:33Z
dc.date.issued 2007-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/83053
dc.description.abstract [EN] One of the aims of domain theory is the construction of an embedding of a given structure or data type as the maximal or “ideal” elements of an enveloping domain of “approximations,” sometimes called a domain environment. Typically the goal is to provide a computational model or framework for recursive and algorithmic reasoning about the original structure. In this paper we consider the function space of (natural equivalence classes of) quasicontinuous functions from a locally compact space X into L, an n-fold product of the extended reals [−1,1] (more generally, into a bicontinuous lattice). We show that the domain of all “approximate maps” that assign to each point of X an order interval of L is a domain environment for the quasicontinuous function space. We rely upon the theory of domain environments to introduce an interesting and useful function space topology on the quasicontinuous function space. We then apply this machinery to define an extended differential calculus in the quasicontinuous function space, and draw connections with viscosity solutions of Hamiltonian equations. The theory depends heavily on topological properties of quasicontinuous functions that have been recently uncovered that involve dense sets of points of continuity and sections of closed relations and USCO maps. These and other basic results about quasicontinuous functions are surveyed and presented in the early sections. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Quasicontinuous functions es_ES
dc.subject USCO maps es_ES
dc.subject Domain theory es_ES
dc.subject Bicontinuous lattices es_ES
dc.subject Generalized calculus es_ES
dc.subject Hamiltonian equations es_ES
dc.subject Viscosity solutions es_ES
dc.title Quasicontinuous functions, domains, and extended calculus es_ES
dc.type Artículo es_ES
dc.date.updated 2017-06-16T10:25:42Z
dc.identifier.doi 10.4995/agt.2007.1908
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Cazacu, R.; Lawson, JD. (2007). Quasicontinuous functions, domains, and extended calculus. Applied General Topology. 8(1):1-33. doi:10.4995/agt.2007.1908. es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2007.1908 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 33 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 8
dc.description.issue 1
dc.identifier.eissn 1989-4147


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