Get Felix Hausdorff - Gesammelte Werke Band III: Mengenlehre PDF

By Felix Hausdorff, Ulrich Felgner, Horst Herrlich, Mirek Husek, Vladimir Kanovei, Peter Koepke, Gerhard Preuß, Walter Purkert, Erhard Scholz

ISBN-10: 3540768068

ISBN-13: 9783540768067

Band III der Hausdorff-Edition enthält Hausdorffs Band „Mengenlehre", seine veröffentlichten Arbeiten zur deskriptiven Mengenlehre und Topologie sowie zahlreiche einschlägige Studien aus dem Nachlaß. Sein Buch „Mengenlehre" erlangte besonders dadurch historische Bedeutung, als darin erstmals eine monographische Darstellung des damals aktuellen Standes der deskriptiven Mengenlehre gegeben wurde. Es ist hier von Spezialisten dieses Gebietes sorgfältig kommentiert worden. Auch die veröffentlichten Arbeiten sind mit ausführlichen Kommentaren versehen. Besonders umfassend ist in diesem Band der variation der Nachlaß Hausdorffs berücksichtigt. Hingewiesen sei insbesondere auf seinen zahlreichen originellen Studien zu Themen der deskriptiven Mengenlehre und auf seine damals sehr originelle Vorlesung über algebraische Topologie vom Sommersemester 1933.

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Extra info for Felix Hausdorff - Gesammelte Werke Band III: Mengenlehre (1927,1935) Deskripte Mengenlehre und Topologie

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A more general corol- lary is the explicit estimate of the common number of zeroes of k polynomials on a k-dimensional separating solution of a system in R"-k of = a"_k = 0 , where all forms al , ... , a"_k n - k Pfaff equations al = have polynomial coefficients (cf. Corollary 4). , polynomials in the coordinate functions x = xl , ... , x" and functions of the form exp(b1, x), sin(cE , X), cos(c, , x) in the region of R" bounded by the inequalities 1(c,, x)l < it. 13 to prove the uniform distribution of the arguments of the complex roots of a polynomial system of equations in which the polynomials have large Newton polyhedra but have a small number of monomials.

For example, in this chapter, "function" should be understood as "infinitely differentiable function". etc. 1. Coorlentation and linking index In this section we recall the definitions and basic properties of the coorientation and linking index. The coorientation of a linear subspace Lk of codimension k in a linear space L is an orientation of the k-dimensional quotient space L/Lk . A coorientation of Lk may be given by fixing a k-form in L that is the product of k independent vectors orthogonal to Lk .

For a P-system with Pchain of length 0 Theorem I follows from Bezout's theorem. Consider the P-system Q, = . = Q" = 0 in R" with P-chain of length k and the equivalent system of equations F, = ... = F" = G = 0 in R"+' with coordinates (XI , ... , x" , v) = (x, v) , where Fj is the function whose value at (x, v) is equal to the value of Q,(x, U1, ... , uk) at (x, u, = fi(x), ... , uk_I = fk_I(x), uk = v) and G(x, v) = fk(x) - v. It follows from the definition of a P-chain that all partial derivatives of the functions Fj and G can be expressed polynomially via the coordinate functions x, v and the functions f in the P-chain.

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Felix Hausdorff - Gesammelte Werke Band III: Mengenlehre (1927,1935) Deskripte Mengenlehre und Topologie by Felix Hausdorff, Ulrich Felgner, Horst Herrlich, Mirek Husek, Vladimir Kanovei, Peter Koepke, Gerhard Preuß, Walter Purkert, Erhard Scholz


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