Determining discrete topology

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Reference no: EM13134653

A covering map is a map p: E -> B with the property that each point b, an element of B, has a neighborhood U such that p^-1(U) is a disjoint union of open sets V_alpha such that, for each alpha, the restriction of p to V_alpha is a homeomorphism of V_alpha onto U.

Show that, if Y has the discrete topology and if p: X x Y --> X is the projection onto the first factor, then p is a covering map.

Reference no: EM13134653

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