Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 225-238

BORSUK–DUGUNDJI TYPE EXTENSION THEOREMS WITH BUSEMANN CONVEX TARGET SPACES

Rafa Espínola, Óscar Madiedo and Adriana Nicolae

University of Seville, Department of Mathematical Analysis - IMUS
Sevilla, Spain; espinola 'at' us.es

Rey Juan Carlos University, Department of Applied Mathematics, ESCET
28933, Móstoles, Spain; oscar.madiedo 'at' urjc.es

University of Seville, Department of Mathematical Analysis - IMUS, Sevilla, Spain
and Babes-Bolyai University, Department of Mathematics
Kogalniceanu 1, 400084 Cluj-Napoca, Romania; anicolae 'at' math.ubbcluj.ro

Abstract. In this work we study continuity properties of convex combinations in Busemann convex geodesic spaces and apply them to obtain two extension results for continuous and Lipschitz mappings with values in a Busemann convex space.

2010 Mathematics Subject Classification: Primary 53C22, 54C20.

Key words: Convex combination, geodesic space, Busemann convexity, extension problem, Lipschitz mapping.

Reference to this article: R. Espínola, Ó. Madiedo and A. Nicolae: Borsuk–Dugundji type extension theorems with Busemann convex target spaces. Ann. Acad. Sci. Fenn. Math. 43 (2018), 225-238.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4313