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Topic: Weierstrass by Willard
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William Elliot

Posts: 2,637
Registered: 1/8/12
Weierstrass by Willard
Posted: Jun 7, 2017 7:13 PM
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On page 292 of General Topology by Stephen Willard
just before definining h(x), it's stated that
|g(x) - g_a(x)| <= 2/3 for x in A1 \/ B1.

I don't see how he got that nor do I understand how to use it.
Could he have meant that
|g(x) - f(x)| <= 2/3 for x in A1 \/ B1?

I think I've a proof of that and it appears useful for the ensuing.

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