Universal Covering Space
If X is a topological space that is path connected, locally path connected and locally simply connected, then it has a simply connected universal covering space on which the fundamental group π(X,x0) acts freely by deck transformations with quotient space X. This space can be constructed analogously to the fundamental group by taking pairs (x, γ), where x is a point in X and γ is a homotopy class of paths from x0 to x and the action of π(X, x0) is by concatenation of paths. It is uniquely determined as a covering space.
Read more about this topic: Fundamental Group
Famous quotes containing the words universal, covering and/or space:
“People get real comfortable with their features. Nobody gets comfortable with their hair. Hair trauma. Its the universal thing.”
—Jamie Lee Curtis (b. 1958)
“Three forms I see on stretchers lying, brought out there untended
lying,
Over each the blanket spread, ample brownish woolen blanket,
Gray and heavy blanket, folding, covering all.”
—Walt Whitman (18191892)
“And Space with gaunt grey eyes and her brother Time
Wheeling and whispering come,”
—James Elroy Flecker (18841919)