Abstract
In this paper, we prove that any convex set in a normed space is $\varepsilon -$proximinal. Consequently, every subspace in a Banach space is $\varepsilon -$proximinal. Some other results of proximinality in tensor product spaces are given.
Highlights
Let X be a Banach space and Y be any subset of X
In this paper we prove that every set in a Banach space is ε−proximinal
Theorem 2.1 shows that the definition of ε− proximinality that was introduced and used in
Summary
Let X be a Banach space and Y be any subset of X. In this paper we prove that every set in a Banach space is ε−proximinal. We prove that every set in a Banach space is ε− proximinal. G is ε−proximinal in X for every ε > 0 This is because, if x ∈ X and x0 is the best approximant of x in G, x − x0 ≤ x − g ≤ x − g + ε. Let E be any set in a Banach space X. Theorem 2.1 shows that the definition of ε− proximinality that was introduced and used in [4], [5] , [6], [7], [8] and [9] is really redundant
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