question: Why would nearly every line of sight end on the surface of a star if we lived in a infinite static universe?
comment: Because in an infinite universe, if you keep going in any direction, *eventually* you're going to hit something. And most of the things out there are stars.
passages: If formula_7, 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.
   If the average density of the universe exactly equals the critical density so that formula_8, then the geometry of the universe is flat: as in Euclidean geometry, the sum of the angles of a triangle is 180 degrees and parallel lines continuously maintain the same distance. Measurements from Wilkinson Microwave Anisotropy Probe have confirmed the universe is flat with only a 0.4% margin of error.
   Intuitively, if one thinks of "S" as of a region surrounded by a wall, "S" is a star domain if one can find a vantage point "x" in "S" from which any point "x" in "S" is within line-of-sight. A similar, but distinct, concept is that of a radial set.
  
  Section::::Examples.
  
  BULLET::::- Any line or plane in R is a star domain.
  
  BULLET::::- A line or a plane with a single point removed is not a star domain.
   However, many authors speak of the “long line” where we have spoken of the (closed or open) long ray, and there is much confusion between the various long spaces. In many uses or counterexamples, however, the distinction is unessential, because the important part is the “long” end of the line, and it doesn't matter what happens at the other end (whether long, short, or closed).
   The greatest known aggregation of these co-located "Junctions" or Terminus Loci occurs in the Manticore binary star system, whose wormholes connect the wormhole junction to six (later seven) other star systems, giving the Manticore system an astrographic position to be coveted, and an immense revenue stream from transit tolls, manufacturing and trade, and a large carrying trade.
   When viewing space from Earth, the attenuation, interstellar dust, and stars in the plane of the Milky Way (the galactic plane) obstruct the view of around 20% of the extragalactic sky at visible wavelengths. As a result, optical galaxy catalogues are usually incomplete close to the galactic plane.
  
  Section::::Modern developments.
   Section::::Role of the shape of the universe.:Closed universe.
  
  If formula_5, then the geometry of space is closed like the surface of a sphere. The sum of the angles of a triangle exceeds 180 degrees and there are no parallel lines; all lines eventually meet. The geometry of the universe is, at least on a very large scale, elliptic.
   All of them are locally compact. None of them is metrisable; this can be seen as the long ray is sequentially compact but not compact, or even Lindelöf.
  
  The (non-extended) long line or ray is not paracompact. It is path-connected, locally path-connected and simply connected but not contractible. It is a one-dimensional topological manifold, with boundary in the case of the closed ray. It is first-countable but not second countable and not separable, so authors who require the latter properties in their manifolds do not call the long line a manifold.
   A related space, the (closed) extended long ray, "L"*, is obtained as the one-point compactification of "L" by adjoining an additional element to the right end of "L". One can similarly define the extended long line by adding two elements to the long line, one at each end.
  
  Section::::Properties.
   In the stellar locus, stars tend to align in a more or less straight feature. If stars were perfect black bodies, the stellar locus would be a pure straight line indeed. The divergences with the straight line are due to the absorptions and emission lines in the stellar spectra. These divergences can be more or less evident depending on the filters used: narrow filters with central wavelength located in regions without lines, will produce a response close to the black body one, and even filters centered at lines if they are broad enough, can give a reasonable blackbody-like behavior.
   The termination shock is the point in the heliosphere where the solar wind slows down to subsonic speed. Even though the termination shock happens as close as 80–100 AU, the maximum extent of the region in which the Sun's gravitational field is dominant (the Hill sphere) is thought to be at around . This point is close to the nearest known star system, Alpha Centauri, located 4.36 light years away. Although the probes will be under the influence of the Sun for a long time, their velocities far exceed the Sun's escape velocity, so they will eventually leave forever.
   Point at infinity
  
  In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
  
  In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added. This holds for a geometry over any field, and more generally over any division ring.
   Cosmologists have long sought to discover whether infinity exists in our physical universe: Are there an infinite number of stars? Does the universe have infinite volume? Does space "go on forever"? This is an open question of cosmology. The question of being infinite is logically separate from the question of having boundaries. The two-dimensional surface of the Earth, for example, is finite, yet has no edge. By travelling in a straight line with respect to the Earth's curvature one will eventually return to the exact spot one started from. The universe, at least in principle, might have a similar topology. If so, one might eventually return to one's starting point after travelling in a straight line through the universe for long enough.
   Topological defects have not been observed by astronomers; however, certain types are not compatible with current observations. In particular, if domain walls and monopoles were present in the observable universe, they would result in significant deviations from what astronomers can see.
   Event horizons can, in principle, arise and evolve in exactly ﬂat regions of spacetime, having no black hole inside, if a hollow spherically symmetric thin shell of matter is collapsing in a vacuum spacetime. The exterior of the shell is a portion of Schwarzschild space and the interior of the hollow shell is exactly ﬂat Minkowski space. Bob Geroch has pointed out that if all the stars in the Milky Way gradually aggregate towards the galactic center while keeping their proportionate distances from each other, they will all fall within their joint Schwarzschild radius long before they are forced to collide. 
   Line at infinity
  
  In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane. The line at infinity is also called the ideal line.
  
  Section::::Geometric formulation.
   The fine topology on the Euclidean space formula_3 is defined to be the coarsest topology making all subharmonic functions (equivalently all superharmonic functions) continuous. Concepts in the fine topology are normally prefixed with the word 'fine' to distinguish them from the corresponding concepts in the usual topology, as for example 'fine neighbourhood' or 'fine continuous'.
  
  Section::::Observations.
   An alternative approach, which makes use of the 'weak anthropic principle', is to suppose that the universe is infinite in size, but with the density varying in different places (i.e. an inhomogeneous universe). Thus some regions will be over-dense and some under-dense . These regions may be extremely far apart - perhaps so far that light has not had time to travel from one to another during the age of the universe (that is, they lie outside one another's cosmological horizons). Therefore, each region would behave essentially as a separate universe: if we happened to live in a large patch of almost-critical density we would have no way of knowing of the existence of far-off under- or over-dense patches since no light or other signal has reached us from them. An appeal to the anthropic principle can then be made, arguing that intelligent life would only arise in those patches with Ω very close to 1, and that therefore our living in such a patch is unsurprising.
   One such observation is that of anisotropies (that is, variations with direction - see below) in the Cosmic Microwave Background (CMB) radiation. The CMB is electromagnetic radiation which fills the universe, left over from an early stage in its history when it was filled with photons and a hot, dense plasma. This plasma cooled as the universe expanded, and when it cooled enough to form stable atoms it no longer absorbed the photons. The photons present at that stage have been propagating ever since, growing fainter and less energetic as they spread through the ever-expanding universe.
   Fine topology (potential theory)
  
  In mathematics, in the field of potential theory, the fine topology is a natural topology for setting the study of subharmonic functions. In the earliest studies of subharmonic functions, namely those for which formula_1 where formula_2 is the Laplacian, only smooth functions were considered. In that case it was natural to consider only the Euclidean topology, but with the advent of upper semi-continuous subharmonic functions introduced by F. Riesz, the fine topology became the more natural tool in many situations.
  
  Section::::Definition.
   In one dimension, that is, on the real line, the fine topology coincides with the usual topology since in that case the subharmonic functions are precisely the convex functions which are already continuous in the usual (Euclidean) topology. Thus, the fine topology is of most interest in formula_3 where formula_5. The fine topology in this case is strictly finer than the usual topology, since there are discontinuous subharmonic functions. 
   In many applications, such as rail, roads, and other transportation networks the network is assumed to be planar. Planar networks build up an important group out of the spatial networks, but not all spatial networks are planar. Indeed, the airline passenger
  
  networks is a non-planar example: All airports in the world are connected through direct flights. 
  
  BULLET::::- The way it is embedded in space
  
  There are examples of networks, which seem to be not "directly" embedded in space. Social networks for instance
  
  connect individuals through friendship relations. But in this case, space intervenes in the fact that the connection
   It makes sense to consider all the long spaces at once because every connected (non-empty) one-dimensional (not necessarily separable) topological manifold possibly with boundary, is homeomorphic to either the circle, the closed interval, the open interval (real line), the half-open interval, the closed long ray, the open long ray, or the long line.
   The midpoint is not naturally defined in projective geometry since there is no distinguished point to play the role of the point at infinity (any point in a projective range may be projectively mapped to any other point in (the same or some other) projective range). However, fixing a point at infinity defines an affine structure on the projective line in question and the above definition can be applied. 
   The definition of a ray depends upon the notion of betweenness for points on a line. It follows that rays exist only for geometries for which this notion exists, typically Euclidean geometry or affine geometry over an ordered field. On the other hand, rays do not exist in projective geometry nor in a geometry over a non-ordered field, like the complex numbers or any finite field.
  
  In topology, a ray in a space "X" is a continuous embedding R → "X". It is used to define the important concept of end of the space.
  
  Section::::Extensions.:Line segment.
  