Abstract
General topology of the universe is described. It is concluded that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than the present topology of the universe. Consequently, the universe remains unbounded. The general topological approach comprises of powerful techniques that could prove to be useful to prescribe mathematical constraints on the global character of the universe as well as on the manifold of space-time.
Highlights
General topology of the universe and its evolutionary aspects are discussed in this paper
In the scenario of universe evolving with time, we conclude that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than the present topology of the universe
One can define a manifold over a topology if that topological space is locally homeomorphic to Rn, which means it is Hausdorff and possesses metric properties, and connectedness is well described in that
Summary
General topology of the universe and its evolutionary aspects are discussed in this paper. It is pertinent to mention that the physical realities of the universe [3]-[8] are in perfect agreement with the mathematical conditions discussed in the present paper. We feel that GTR and Einstein equation describe the universe in a specific physical scenario of a theoretical framework, whereas, general topology of the whole space is absolute truth, and it is not limited to any specific physical scenario This discussion addresses the boundary of the universe, and a detail spatial analysis of the universe with reference to open space, closed space, boundary, compactness, connectedness, limit points, frontier points, interior points, topological transitions and causality and topology. It is concluded in this paper that the general topology of the whole space could be a very good philosophical basis for describing geometry of the universe as it prescribes mathematical constraints on the global geometry of the universe. The metric of the universe is closed but it cannot be bounded, and it is not at all compact
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