Now, we need to give ~X a topology that makes p into a covering map (so we need to show that every point in X has an evenly covered neighborhood, and that p is continuous).

Let p : ̄X → X be a covering map. If α, β : [0, 1] → ̄X are two continuous paths with α(0) = β(0) and [p α] = [p β], then [α] = [β]; in particular α(1) = β(1).

In this note, we sketch a few properties of covering numbers, VC-dimension, and provide a few pointers to more general resources for more detailed treatment of the results.

By choosing orientations on each 1-cell of the bouquet, we can build a covering map by sending the vertices above to the vertex, and the arcs to the one cells, homeomorphically, respecting the …

We rst introduce the concept of packing, covering, relate them to the notion of volume, and then plug them into the lower bound obtained using the Fano's inequality.

bstract. We introduce the theory of covering spaces, with emphasis on explaining the Galois correspondence of covering spaces and the deck trans-formati. n group. We focus especially on the …

Covering Manif smooth manifolds. A smoo h surjection : ~M! M is called a coverin = t U and jU : U! U is a di eo orphism for each . The manifold ~M is called a cove is evenly covered. Compare this de nition …