Remarks About Some Weierstrass Type Results

Authors: MIHAI TURINICI

Abstract: The Weierstrass type results of Gajek and Zagrodny [7] are not in general retainable in the precise context. Our first aim in this exposition is to show that a completion of the imposed conditions may be offered so that these results be true. As a second aim, alternate proofs of the statements in question are performed, via ordering principles comparable with the one in Brezis and Browder [3].

Keywords: Relation, maximal element, extremal value, monotonically semicontinuous function, compact metric space, Brezis-Browder ordering principle, countably ordered structure

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