If p : E → B is a continuous surjection between completely regular spaces E and B, we may apply the Stone-Čech compactification functor β to obtain a surjection βp : βE → βB. It is well-known that if E = B × F where F is a finite set and p is projection on the first factor, then βE = βB × βF , and βp is again projection on the first factor. In this paper, we apply β to an n-fold covering map, t...

4-branes that wrap the long and short fundamental 1-cycles of a rectangular toroidal orbifold T 2 /(Z2) 3 , which has Planck-scale compactification radii, intersect after 43 and 109 wrappings, respectively, in a 3-brane upon which the scale factor, equal to a power of the inverse of compactification length, has precisely the same value when measured parallel to either of the fundamental 1-cycle...

We show that if a knot exterior satisfies certain conditions, then it has finite cyclic coverings with arbitrarily large numbers of nontrivial algebraic components in their SL2(C)-character varieties (Theorem A). As an example, these conditions hold for hyperbolic punctured torus bundles over the circle (Theorem B). We investigate in more detail the finite cyclic covers of the figure-eight knot...

Suppose M is a connected, open, orientable, irreducible 3-manifold which is not homeomorphic to R. Given a compact 3-manifold J in M which satisfies certain conditions Brin and Thickstun have associated to it an open neighborhood V called an end reduction of M at J . It has some useful properties which allow one to extend to M various results known to hold for the more restrictive class of even...

In this paper, we identify a fundamental algorithmic problem that we term space-constrained dynamic covering (SCDC), arising in many modern-day web applications, including ad-serving and online recommendation systems in eBay and Netflix. Roughly speaking, SCDC applies two restrictions to the well-studied Max-Coverage problem [9]: Given an integer k, X = {1, 2, . . . , n} and I = {S1, . . . , Sm...