caa a22 4500 388092629 CHVBK 20180307125255.0 cr unu---uuuuu 161130e199912 xx s 000 0 eng 10.1017/S0004972700036601 doi S0004972700036601 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700036601 Slice convergence of parametrised sums of convex functions in non-reflexive spaces [Elektronische Daten] The objectives of this study of slice convergence are two-fold. The first is to derive results regarding the passage of certain semi-convergences through Young-Fenchel conjugation. These semi-convergences arise from the splitting of the usual slice topology in the primal and dual spaces into (non-Hausdorff) topologies: the upper slice topology ; a topology generating a convergence closely resembling the bounded-weak* upper Kuratowski convergence; along with the respective primal and dual lower Kuratowski topologies. This gives rise to topological convergences not reliant on sequentially-based definitions found in many such studies, and associated topological continuity results for conjugation (in normed spaces), in contrast to the usual sequential continuity exhibited by analogues of Mosco convergence. The second objective is to study the passage of slice convergence through addition. Such sum theorems have been derived in other works and we establish previous theorems from a unified framework as well as obtaining a new result. Copyright © Australian Mathematical Society 1999 Wenczel Robert E-mail: andy.eb@rmit.edu.au Eberhard Andrew E-mail: andy.eb@rmit.edu.au Bulletin of the Australian Mathematical Society Cambridge University Press 60/3(1999-12), 429-458 0004-9727 60:3<429 1999 60 BAZ https://doi.org/10.1017/S0004972700036601 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700036601 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wenczel Robert E-mail: andy.eb@rmit.edu.au NATIONALLICENCE 700 1- Eberhard Andrew E-mail: andy.eb@rmit.edu.au NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/3(1999-12), 429-458 0004-9727 60:3<429 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge