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" The proof of this theorem is completely analogous to the proof of Theorem 8, Chapter VII, and need not be repeated here. "
Projective Geometry - Page 266
by Oswald Veblen, John Wesley Young - 1910
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PROJECTIVE GEOMETRY

OSWALD VEBLEN - 1910
...into lines by equations of the form (1) B = a 3l x 1 where the determinant A of the coefficients a {j is different from zero. Conversely, every transformation...corollary we have COROLLARY 1. The transformation pu[~x^ pu! 2 ~ x 2 , pu^== x 3 in a plane represents a polarity in which to every side of the triangle...
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Fourteen Papers on Logic, Algebra, Complex Variables and Topology

Algebra - 1965 - 396 pages
...elements xv . . . , Xrt, satisfying the conditions p^j-...-p^.o, *&-..*n *0. Then g(E, B, F, p) > o + 1. The proof of this theorem is completely analogous to the proof of Theorem 4 of the note [1]. 5. Universal principal fiber spaces of genus n. Suppose that G is a topological...
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Twelve Papers on Functional Analysis and Geometry

Mathematics - 1969 - 258 pages
...then (1 - \A) 1 is an integral operator- function of order not greater than r and of minimal type. The proof of this theorem is completely analogous to the proof of Theorem 2.1. In this connection it is necessary to consider only that for the conditions of the theorem det(l...
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Six papers in analysis, Volume 101

Boris Moiseevich Levitan Vladimir Aleksandrovich Marchenko Boris Leonidovich Rozhdestvenskiĭ - Differential equations - 1973 - 250 pages
...^{2ift2fti} (A2 = '/ A , = ) /sa transformation operator defined on the set *JDf |'0 e). The proof of this theorem is completely analogous to the proof of Theorem 3.1.1, and is omitted. We observe only that from the proof of Theorem 3.1. Г it follows that the transformation...
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Some Questions in Constructive Functional Analysis, Issue 114

Phan Dnh Diu - Mathematics - 1974 - 228 pages
...and T'separated. 4.2.1. If a locally convex space 3D is enumerably normable, then it is metrizable. The proof of this theorem is completely analogous to the proof of the corresponding theorem in classical functional analysis (see, for example, [7], Chapter XI). Now...
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Symbolic and Algebraic Computation: International Symposium ISSAC' 88, Rome ...

Patrizia Gianni - Computers - 1989 - 543 pages
...Euler product. Theorem 4 Co, = flp(1 _ )1, where the product is taken over all prime ideals P in O. The proof of this theorem is completely analogous to the proof of Theorem 2. Finally if we define t for O as we did for Z, we get the following inversion theorem. Theorem...
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Eight Papers on Differential Equations and Functional Analysis

Differential equations - 1966 - 295 pages
...or 6* ; f. Im A, (a) = 0 only for a = a. or only for a = h., and at that point A'Дff) = -tan1. The proof of this theorem is completely analogous to the proof of Theorem 5. After this the prohlem of ohtaining asymptotics for E(x, y) in a neighhorhood of a special direction...
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Transactions of the Moscow Mathematical Society

American Mathematical Society - 1992 - 373 pages
...Incapacity (a> n - 2m) is as small as we please, so that u turns out to be continuous on the remaining set. The proof of this theorem is completely analogous to the proof of Luzin's Theorem and proceeds by means of Lemma 1.8. (3.1) (G)' where C does not depend on u. This inequality...
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Eleven Papers on Analysis

Mathematical analysis - 1966 - 284 pages
...the classes KR or К(ш). Then the operator Jc0 is bounded from below in ij^m^ and s(0)=[0, т). The proof of this theorem is completely analogous to the proof of Theorems 3.1 and 3.3 and teduces to a reference to Theorems 1.1, 1.2, 2.2 and 2.3. We now have an analog...
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Theory of Entire and Meromorphic Functions: Deficient and Asymptotic Values ...

Guan-hou Zhang - Mathematics - 1993 - 375 pages
...the above hypothesis, there exists a curve L tending continuously to oo in region Dp , such that lim The proof of this theorem is completely analogous to the proof of Theorem 4. 14 in the sequel. 4.2. The Denjoy Conjecture 4.2.1. The Denjoy Conjecture. In 1907, A Denjoy made...
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