Hausdorff separability of the boundaries for spacetimes and sequential spaces

Autor(es)

Flores, J. L. ^[1] ; Herrera, J. ^[2] ; Sanchez, M. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Malaga, Fac Ciencia, Dept Algebra Geomet & Topol, Campus Teatinos, E-29071 Malaga - Spain

^[2] Univ Fed Santa Catarina, Dept Matemat, BR-88040900 Florianopolis, SC - Brazil

^[3] Univ Granada, Fac Ciencias, Dept Geomet & Topol, Ave Fuentenueva S-N, E-18071 Granada - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 57, n. 2 FEB 2016.
• Citações Web of Science: 4

Resumo

There are several ideal boundaries and completions in general relativity sharing the topological property of being sequential, i.e., determined by the convergence of its sequences and, so, by some limit operator L. As emphasized in a classical article by Geroch, Liang, and Wald, some of them have the property, commonly regarded as a drawback, that there are points of the spacetime M non-T-1-separated from points of the boundary. M. Here, we show that this problem can be solved from a general topological viewpoint. In particular, there is a canonical minimum refinement of the topology in the completion M which T-2-separates the spacetime M and its boundary partial derivative M - no matter the type of completion one chooses. Moreover, we analyze the case of sequential spaces and show how the refined T-2-separating topology can be constructed from a modification L{*} of the original limit operator L. Finally, we particularize this procedure to the case of the causal boundary and show how the separability of M and. M can be introduced as an abstract axiom in its definition. (C) 2016 AIP Publishing LLC. (AU)

• Processo FAPESP: 12/11950-7 - Tópicos em Relatividade Matemática
• Beneficiário: Jónatan Herrera Fernández
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado