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Let X = { x, y, z }. Let the list of open sets of X...

Let X = { x, y, z }. Let the list of open sets of X be Z1. Z1 = { {}, {x}, X }. Let Y = { a, b, c }. Let the list of open sets of Y be Z2. Z2 = { {}, {a, b}, Y }.

Let f : X --> Y be defined as follows: f (x) = a, f (y) = b, f(z) = c

Is f continuous? Prove or disprove using the topological definitions of continuity.

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