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The paradox is that a static, infinitely old universe with an infinite number of stars distributed in an infinitely large space would be bright rather than dark. [1] A view of a square section of four concentric shells. To show this, we divide the universe into a series of concentric shells, 1 light year thick.
An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other.
In cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contracting. Such a universe does not have so-called spatial curvature; that is to say that it is 'flat' or ...
If <, the geometry of space is open, i.e., negatively curved like the surface of a saddle. The angles of a triangle sum to less than 180 degrees, and lines that do not meet are never equidistant; they have a point of least distance and otherwise grow apart. The geometry of such a universe is hyperbolic. [11]
Deep space is defined by the United States government as all of outer space which lies further from Earth than a typical low-Earth-orbit, thus assigning the Moon to deep-space. [117] Other definitions vary the starting point of deep-space from, "That which lies beyond the orbit of the moon," to "That which lies beyond the farthest reaches of ...
Physicists have not reached a consensus about what actually happens at the extreme densities predicted by singularities (including at the start of the Big Bang). [ 5 ] General relativity predicts that any object collapsing beyond a certain point (for stars this is the Schwarzschild radius ) would form a black hole, inside which a singularity ...
Because humans cannot observe space beyond the edge of the observable universe, it is unknown whether the size of the universe in its totality is finite or infinite. [3] [57] [58] Estimates suggest that the whole universe, if finite, must be more than 250 times larger than a Hubble sphere. [59]
However, this is not implied by the abstract definition of a vector space, and vector spaces of infinite dimension can be considered. This is typically the case in functional analysis where function spaces are generally vector spaces of infinite dimension. In topology, some constructions can generate topological spaces of infinite dimension.