A Topology for the Abstract Boundary Construction of Space-time
Richard Barry
(Australian National University)
Coauthor(s): Susan M. Scott
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The abstract boundary construction produces a boundary for an n-dimensional manifold in such a way that this boundary is independent of any particular embedding. In effect, this is done by considering all possible embeddings of a manifold. This boundary then allows for various types of boundary points, such as 'singularities' and 'points at infinity' to be defined. Due to the way in which the abstract boundary is constructed, it is of particular importance to understand how boundary points of one embedding are related to boundary points of another embedding. A topology which encapsulates some of this information would therefore be highly useful, and would aid in the construction of 'optimal embeddings' of space-times, i. e. , embeddings of space-times that clearly display all of their important physical features, like singularities. A possible topology that exhibits this behaviour, and its properties, will be discussed.