Difference between revisions of "12-240/Classnotes for Thursday October 11"

From Drorbn
Jump to: navigation, search
(corollaries)
Line 12: Line 12:
  
 
== corollaries ==
 
== corollaries ==
 +
1/ If V has a finite basic β1, then any other basic β2 of V is also finite and |β1|=|β2|
 +
 +
2/ "dim V" makes sense
 +
 +
dim V =  |β| if V has a finite basic β
 +
 +
Otherwise, dim V = <math>\infty \!\,</math>
 +
 +
ex: dim P(F)= <math>\infty \!\,</math>
  
 
== Lecture notes scanned by [[User:Oguzhancan|Oguzhancan]] ==
 
== Lecture notes scanned by [[User:Oguzhancan|Oguzhancan]] ==

Revision as of 16:33, 12 October 2012

In this lecture, the professor concentrate on corollaries of basic and dimension.

Annoucements

TA Office Hours (Still pending!) @ 215 Huron St., 10th floor.

Peter - 11am - 1pm

Brandon 1pm - 3pm

Topic: Replacement Theorem

corollaries

1/ If V has a finite basic β1, then any other basic β2 of V is also finite and |β1|=|β2|

2/ "dim V" makes sense

dim V = |β| if V has a finite basic β

Otherwise, dim V = \infty \!\,

ex: dim P(F)= \infty \!\,

Lecture notes scanned by Oguzhancan