The Weierstrass type results of Gajek and Zagrodny  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 .
TURINICI, MIHAI (2006) "Remarks About Some Weierstrass Type Results," Turkish Journal of Mathematics: Vol. 30: No. 4, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol30/iss4/4