By Pickert G.

Show description

Read Online or Download Analytische Geometrie PDF

Best geometry and topology books

The Geometry of Rene Descartes

The nice paintings that based analytical geometry. incorporated this is the unique French textual content, Descartes’ personal diagrams, including the definitive Smith-Latham translation. "The maximum unmarried step ever made within the growth of the precise sciences. "— John Stuart Mill.

Extra resources for Analytische Geometrie

Example text

H = T* - are precisely the replete spaces. As a special case, one sees that compact spaces have this property. e. 5-4)). 5-2) fact that homeomorphic spaces S continuous functions was noted. 5-l), yet C(UT,I_I) is always the same as C(T,F$. Still, there is a result going in the converse direction. If C(S,R) is isomorphic to C(T,R), then the characters of the algebras are also identifiable, hence so are vS and UT - at least in the sense that they are in 1-1 correspondence. But this is rather weak.

For T with respect to which each x c is the weakest uniform structure C(T,R) is uniformly continuous). (b) UT consists of those points p € BT such that for all sequences (Vn) of neighborhoods of p in BT, (nVn)n T # @. Thus p $' UT if and only if there is some G6 set (in BT) containing p which does not meet T. Proof and ? e. the initial uniformity determined on UT by the functions for x € C(T,F$. We show that UT is the C-completion of T. -complete. ) To show that UT is C-complete, it suffices (see for example Bourbaki 1966a.

ALGEBRAS O F CONTINUOUS F U N C T I O N S Let e denote the identity of C(T,R), the mapping sending each t c T into 1. To see that the map p + p* is onto H, let h be any character. There exists p c BT such that ker h = p , whence h Q uT, for then ker h = ker p* = M consider any x c C(T,F$ show that x B (p) F. P M P and it remains only to show that = p*. To see that p c uT, and its continuous extension xB c C(BT,FU(m]); As x-h(x)e c ker h = we M P p c cl z(x-h(x)e). B Hence there must be a net (t ) from (z(x-h(x)e) converging to p.

Download PDF sample

Rated 4.85 of 5 – based on 42 votes