Ideal convergence in locally solid Riesz spaces
Author(s) -
Bipan Hazarika
Publication year - 2014
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1404797h
Subject(s) - mathematics , ideal (ethics) , pure mathematics , convergence (economics) , space (punctuation) , bounded function , riesz representation theorem , locally compact space , sequence (biology) , discrete mathematics , mathematical analysis , philosophy , linguistics , epistemology , biology , economics , genetics , economic growth
An ideal $I$ is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper, we introduce the concepts of ideal $\tau$-convergence, ideal $\tau$-Cauchy and ideal $\tau$-bounded sequence in locally solid Riesz space endowed with the topology $\tau.$ Some basic properties of these concepts has been investigated. We also examine the ideal $\tau$-continuity of a mapping defined on locally solid Riesz space.
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