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Proof It is obvious that G is continuous in view of continuity of f, I k and I k ∗.
By the continuity of g, we have G is continuous.
On the other hand, by the continuity of f we know the operator G is continuous.
T is continuous, G is continuous and commutes with T or. ( X, d, ≤ ) is regular and G ( X ) is closed.
Then g is continuous.
Clearly G is continuous.
That is, G is continuous.
Thus G is continuous on B N ¯.
f or g is continuous, or.
Then the function g is continuous.
This means that G is continuous.
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