Normed Interval Space and Its Topological Structure

Hsien-Chung Wu
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Hsien-Chung Wu: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan

Mathematics, 2019, vol. 7, issue 10, 1-22

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.

Keywords: interval space; open sets; norms; null set; open balls (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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