Let X be some topological space. Let A be a subspace of X. I am thinking about the following: If f is a cts function from X to X, and g a cts function from X to A, when is the piece-wise function(adsbygoogle = window.adsbygoogle || []).push({});

h(x) = f(x) if x is not in A, g(x) if x is in A

continuous? My intuition tells me they must agree on the closure (or maybe boundary?) of A? If not, any idea?

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# General question regarding continuous functions and spaces

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