caa a22 4500 388092262 CHVBK 20180307125255.0 cr unu---uuuuu 161130e199908 xx s 000 0 eng 10.1017/S0004972700033359 doi S0004972700033359 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700033359 Beer Gerald Department of Mathematics California State University Los Angeles CA 90032 United States of America Quasi-concave functions and convex convergence to infinity [Elektronische Daten] [Gerald Beer] By a convex mode of convergence to infinity 〈Ck〉, we mean a sequence of nonempty closed convex subsets of a normed linear space X such that for each k, Ck+1 ⊆ int Ck and and a sequence 〈xn〉 is X is declared convergent to infinity with respect to 〈Ck〉 provided each Ck contains xn eventually. Positive convergence to infinity with respect to a pointed cone with nonempty interior as well as convergence to infinity in a fixed direction fit within this framework. In this paper we study the representation of convex modes of convergence to infinity by quasi-concave functions and associated remetrizations of the space. Copyright © Australian Mathematical Society 1999 Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 81-94 0004-9727 60:1<81 1999 60 BAZ https://doi.org/10.1017/S0004972700033359 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700033359 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Beer Gerald Department of Mathematics California State University Los Angeles CA 90032 United States of America NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 81-94 0004-9727 60:1<81 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge