Algebraic operations on the space of Hausdorff continuous interval functions

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dc.creatorAnguelov, Roumen
dc.creatorMarkov, Svetoslav
dc.creatorSendov, Blagovest
dc.date2005-12-13
dc.date.accessioned2026-07-07T06:55:08Z
dc.date.available2026-07-07T06:55:08Z
dc.descriptionWe show that the operations addition and multiplication on the set $C(Ω)$ of all real continuous functions on $Ω\subseteq\mathbb{R}^n$ can be extended to the set $\mathbb{H}(Ω)$ of all Hausdorff continuous interval functions on $Ω$ in such a way that the algebraic structure of $C(Ω)$ is preserved, namely, $\mathbb{H}(Ω)$ is a commutative ring with identity. The operations on $\mathbb{H}(Ω)$ are defined in three different but equivalent ways. This allow us to look at these operations from different points of view as well as to show that they are naturally associated with the Hausdorff continuous functions.
dc.identifierhttps://arxiv.org/abs/math/0512272
dc.identifierhttp://arxiv.org/abs/math/0512272
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106186
dc.subjectGeneral Mathematics
dc.subjectClassical Analysis and ODEs
dc.subject26E99; 54C35
dc.titleAlgebraic operations on the space of Hausdorff continuous interval functions
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