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Continuity of family of 1-parameter maps in Milnor's Morse theory

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In the proof of Theorem 16.3 in Milnor's Morse Theory (see. pp. 91), he writes "It is easily verified that $r_u(\omega)$ is continuous as a function of both variables." I'm struggling to see why this is the case, so if someone could help me out (I suspect it's a one-line argument) I would greatly appreciate it.


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