caa a22 4500 386371962 CHVBK 20180307112001.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S0017089500007540 doi S0017089500007540 pii (NATIONALLICENCE)cambridge-10.1017/S0017089500007540 Nawrocki Marek Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland On weak approximation and convexification in weighted spaces of vector-valued continuous functions [Elektronische Daten] [Marek Nawrocki] Let X be a completely regular Hausdorff space. A Nachbin family of weights is a set V of upper-semicontinuous positive functions on X such that if u, υ V then there exists w V and t > 0 so that u, υ ≤ tw. For any Hausdorff topological vector space E, the weighted space CV0(X, E) is the space of all E-valued continuous functions f on X such that υf vanishes at infinity for all υ V. CV0(X, E) is equipped with the weighted topology wv = wv(X, E) which has as a base of neighbourhoods of zero the family of all sets of the form where υ Vand W is a neighbourhood of zero in E. If E is the scalar field, then the space CV0(X, E) is denoted by CV0(X). The reader is referred to [4, 6, 8] for information on weighted spaces. Copyright © Glasgow Mathematical Journal Trust 1989 Glasgow Mathematical Journal Cambridge University Press 31/1(1989-01), 59-64 0017-0895 31:1<59 1989 31 GMJ https://doi.org/10.1017/S0017089500007540 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0017089500007540 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Nawrocki Marek Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland NATIONALLICENCE 773 0- Glasgow Mathematical Journal Cambridge University Press 31/1(1989-01), 59-64 0017-0895 31:1<59 1989 31 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge