Real function/Continuous/Rules/Section
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Let and be subsets and let
and
denote functions with
. Then the following statements hold.- If is continuous in and is continuous in , then also the composition is continuous in .
- If and are continuous, so is .
The first statement follows from fact. This implies also the second statement.
Let be a subset and let
be continuous functions. Then also the functions
are continuous. For a subset such that has no zero in , also
is continuous.
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