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The second set is compact, since it is the image of a closed and bounded set under a continuous mapping.
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If (( X,M ) ) is an (FMS) under some t-norm, then M is a continuous mapping on (X^{2}times 0,infty)).
Clearly is a continuous mapping.
Let be a linear mapping and be a continuous mapping.
(phi') is a continuous mapping from (N') to (M').
Similarly, we also define a continuous mapping.
Thus, T is continuous under the norm ∥ ⋅ ∥ c 0. Summarizing all the above, we see that T is a continuous mapping from the compact convex subset X ( I, M ) of the Banach space C 0 ( I, R ) into itself.
Step 3: (mathcal{A}) is a continuous mapping.
Let (A: Krightarrow R^{n}) be a continuous mapping.
Hence, let (gcolon Ato A) be a continuous mapping.
Let (A: Krightarrow X^) be a continuous mapping.
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