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Normed Interval Space and Its Topological Structure

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  • Hsien-Chung Wu

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan)

Abstract

Based on the natural vector addition and scalar multiplication, the set of all bounded and closed intervals in R cannot form a vector space. This is mainly because the zero element does not exist. In this paper, we endow a norm to the interval space in which the axioms are almost the same as the axioms of conventional norm by involving the concept of null set. Under this consideration, we shall propose two different concepts of open balls. Based on the open balls, we shall also propose the different types of open sets, which can generate many different topologies.

Suggested Citation

  • Hsien-Chung Wu, 2019. "Normed Interval Space and Its Topological Structure," Mathematics, MDPI, vol. 7(10), pages 1-22, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:983-:d:277253
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    References listed on IDEAS

    as
    1. Hsien-Chung Wu, 2011. "Duality Theory in Interval-Valued Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 298-316, August.
    2. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
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