Barry, Richard A.; Scott, Susan M. The strongly attached point topology of the abstract boundary for space-time. (English) Zbl 1297.83027 Classical Quantum Gravity 31, No. 12, Article ID 125004, 24 p. (2014). Summary: The abstract boundary construction of Scott and Szekeres provides a ‘boundary’ for any n-dimensional, paracompact, connected, Hausdorff, \({C}^{\infty}\) manifold. Singularities may then be defined as objects within this boundary. In a previous paper [R. A. Barry and S. M. Scott, Classical Quantum Gravity 28, No. 16, Article ID 165003, 14 p. (2011; Zbl 1226.83005)], a topology referred to as the attached point topology was defined for a manifold and its abstract boundary, thereby providing us with a description of how the abstract boundary is related to the underlying manifold. In this paper, a second topology, referred to as the strongly attached point topology, is presented for the abstract boundary construction. Whereas the abstract boundary was effectively disconnected from the manifold in the attached point topology, it is very much connected in the strongly attached point topology. A number of other interesting properties of the strongly attached point topology are considered, each of which support the idea that it is a very natural and appropriate topology for a manifold and its abstract boundary. Cited in 2 Documents MSC: 83C75 Space-time singularities, cosmic censorship, etc. 57R40 Embeddings in differential topology 54F65 Topological characterizations of particular spaces 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems) 53Z05 Applications of differential geometry to physics Keywords:point topology; abstract boundary; space-time; singularities Citations:Zbl 1226.83005 PDFBibTeX XMLCite \textit{R. A. Barry} and \textit{S. M. Scott}, Classical Quantum Gravity 31, No. 12, Article ID 125004, 24 p. (2014; Zbl 1297.83027) Full Text: DOI arXiv