# Download e-book for kindle: A Beckman-Quarles type theorem for finite desarguesian by Benz W.

By Benz W.

Read Online or Download A Beckman-Quarles type theorem for finite desarguesian planes PDF

Similar geometry and topology books

New PDF release: Real Methods in Complex and CR Geometry: Lectures given at

The geometry of genuine submanifolds in complicated manifolds and the research in their mappings belong to the main complex streams of latest arithmetic. during this zone converge the thoughts of assorted and complex mathematical fields similar to P. D. E. 's, boundary worth difficulties, brought about equations, analytic discs in symplectic areas, advanced dynamics.

Download e-book for kindle: Das Zebra-Buch zur Geometrie by Prof. Ferdinand Verhulst, Prof. Dr. Sebastian Walcher

In den Niederlanden erscheint seit etwa zehn Jahren die erfolgreiche "Zebra-Reihe" mit Broschüren zu Mathematik fuer Projekte und selbstgesteuertes Lernen. Die Themen sind ohne vertiefte Vorkenntnisse zugänglich und ermöglichen eigenes Erforschen und Entdecken von Mathematik. Die Autoren der Bände sind Schulpraktiker, Mathematikdidaktiker und auch Fachwissenschaftler.

Extra info for A Beckman-Quarles type theorem for finite desarguesian planes

Example text

Then Cco(z)c CPCO(z). Since e E Y C X ( ~ E Owe ) , have Cco(z)C CPco(z) C X \ K and so z E X(EO). Since f ( Y )= Y , we have nm(p-l)co(~)) cn cY 00 Yc 00 m(Eo)) i=O i=O nzo and thus Y = fi(N(p-l)co(Y)). Since C ( p - l ) c o ( zC) Cclco(z) C X \ K for C x ( , - l ) c 0 ( f ( ~and ) ) thus f(N(P--l)CO L E Y , we have f ( C ( P - l ) c o ( z3) ) ( Y ) )3 N x ( P - l ) c o ( y ) 3 ~(jA-1)co(Y). Therefore, Y = N(P-l)co(Y) and Y is open in X. This is a contradiction. 21. Consider the subset X in the plane defined by x = {% : I%[ 3 1 = 1) u {% : 1% - -1 = -} 2 2 u {% : 1% + -132 1 = -}.

This is followed by defining a Lyapunovfunction V((zl, y l ) , ( X 2 , Y Z ) ) by = -(Y2 - Y l ) ( Y 2 - 2 2 - ( Y l - x1)). 2 Anosov differentiable systems 25 In fact, V : T2 x T2 4 R is continuous, V(z',z')= 0 for z' E T2 and V(g(z'), g(y')) -V(z',y') > 0 whenever 0 < d(z',y') 5 a for a > 0 small enough. Then g is expansive. This is easily checked as follows. Let 0 < e < a. Then e is an expansive constant for 9. Indeed, suppose 3: # y and d(g"(z),g"(y)) 5 e for all n E %. Since T2 is compact, there exists 6 > 0 such that for u,v E T2 ).

N;=, u,"==, In the remainder of this section we describe well known theorems that will be used in the sequel. Let X be a topological space. A path in X is a continuous map from the unit interval [0,1] to X. If any two points in X are joined by a path, then X is said to be path connected. In general, a connected space need not be path connected. An arc in X is an injective continuous map from [0,1] to X. We say that X is arcwise connected if any two points in X are joined by an arc. It is clear that if X is arcwise connected then it is path connected.