What is the character of space? (booklet)
Topology: the study of those properties of geometric forms that remain invariant under certain transformations, as bending or stretching. (on-line dictionary definition)
2.13 The Topology of Space Einstein’s field equations, and others like them, are second order partial differential equations that in nature are local. A full solution normally requires the assumption of boundary conditions, which in cosmology are in most cases unknown. One could argue, with Einstein and Wheeler, that the universe should therefore have no boundary. For example, in a k = +1 standard cosmology, the space has the shape of a sphere, so light can travel around it (Misner, Thorne and Wheeler 1973). This can be tested astrophysically, for example by looking for multiple images of the same galaxy. A similar argument applies to connectivity. Parts of one space may in principle be connected to the same space or another by wormholes; and it is possible to construct cosmological models where the universe consists of juxtaposed cells, a periodicity which can be looked for using astronomical data (Hayward and Twamley 1990). This is in 4D. In N ≥ 5D, the possibilities are even more extensive, and there was mentioned in the preceding Section the case of a flat 5D space that can contain curved 4D spaces. There is hardly any information on the topology, and connectivity, of space.?
-- FUNDAMENTAL UNSOLVED PROBLEMS IN PHYSICS AND ASTROPHYSICS Paul S. Wesson Department of Physics University of Waterloo Waterloo, Ontario N2L 3G1 Canada prepared for California Institute for Physics and Astrophysics 366 Cambridge Avenue Palo Alto, California 94306 U.S.A. Email: [email protected]?
(calphysics.org/problems.pdf)
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Chapter 1. ?Is matter made from space? | LinkedIn