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Geological Society, London, Special Publications; 2006; v. 264; p. 203-206;
DOI: 10.1144/GSL.SP.2006.264.01.15
© 2006 Geological Society of London

General Theory and Methods

Is the simplex open or closed? (some topological concepts)

E. Barrabés & G. Mateu-Figueras

Department Informàtica i Matemàtica Aplicada, Universitat de Girona, Campus Montilivi, P4, E-17071 Girona, Spain

(e-mail: barrabes{at}ima.udg.es)

The simplex is the natural space to work with when compositional data are considered. Sometimes, the concepts of open simplex and closed simplex are used, although most of the time they are not well defined. The objective of this contribution is to expose some of the mathematical concepts related to the simplex and its structure in order to make clear when the terms open and closed are mathematically appropriate. Moreover, these concepts sometimes generate discussion about the proper representation of the simplex. It will be shown that this discussion makes no sense when considering the simplex as a Euclidean vector space.