Partial Differentiation on Normed Linear Spaces Rn
نویسندگان
چکیده
Let i, n be elements of N. The functor proj(i, n) yielding a function from Rn into R is defined by: (Def. 1) For every element x of Rn holds (proj(i, n))(x) = x(i). Next we state two propositions: (1) dom proj(1, 1) = R1 and rng proj(1, 1) = R and for every element x of R holds (proj(1, 1))(〈x〉) = x and (proj(1, 1))−1(x) = 〈x〉. (2)(i) (proj(1, 1))−1 is a function from R into R1, (ii) (proj(1, 1))−1 is one-to-one, (iii) dom((proj(1, 1))−1) = R, (iv) rng((proj(1, 1))−1) = R1, and
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