On Filter $(\alpha)$-convergence and Exhaustiveness of Function Nets in Lattice Groups and Applications | Zendy

Antonio Boccuto | Zendy; Xenofon Dimitriou | Zendy

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On Filter $(\alpha)$-convergence and Exhaustiveness of Function Nets in Lattice Groups and Applications

Author(s) -

Antonio Boccuto,

Xenofon Dimitriou

Publication year - 2015

Publication title -

journal of mathematics research

Language(s) - English

Resource type - Journals

eISSN - 1916-9809

pISSN - 1916-9795

DOI - 10.5539/jmr.v7n2p56

Subject(s) - mathematics , pointwise , pointwise convergence , filter (signal processing) , lattice (music) , context (archaeology) , discrete mathematics , pure mathematics , combinatorics , topology (electrical circuits) , mathematical analysis , network topology , computer science , paleontology , physics , acoustics , computer vision , biology , operating system

We consider (strong uniform)continuity of thelimit of a pointwise convergent net of latticegroup-valued functions, (strong weak)ex\-hau\-sti\-ve\-ness and (strong)$(\alpha)$-con\-ver\-gen\-ce with respect to a pairof filters, which in the setting of nets aremore natural than the corresponding notionsformulated with respect to a single filter. Somecomparison results are givenbetween such concepts, inconnection with suitable properties of filters.Moreover, some modes of filter(strong uniform) continuity for lattice group-valuedfunctions are investigated, givingsome characterization.As an application, we getsome Ascoli-type theorem in an abstract setting,extending earlier results to the context of filter$(\alpha)$-con\-ver\-gen\-ce.Furthermore, we pose some open problems.

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