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Definition: Let X and Y be spaces, Y be compact, and N be an open set of X x Y containing the "slice" (x_0, Y) of X x Y. If W is a neighborhood of x_0 in X such that N contains the entire set W x Y, then we denote W x Y to be a tube about (x_0, Y).
Source: Topology (second edition) by James R. Munkres