? normed space and metric space
Hi:
What are the differences between a normed space and a metric space?
I thought a metric space means a space that comes with the "distance"
being defined, and likewise a normed space with a norm being defined.
But isn't norm kind of distance? Any differences?
Thanks,
by Cheng Cosine
Feb/17/2k8 NC
.
Relevant Pages
 Re: ? normed space and metric space
... I thought a metric space means a space that comes with the "distance" ... and likewise a normed space with a norm being defined. ... But isn't norm kind of distance? ... (sci.math)  Why Topology? (was irrationality 0.201201020100201000201...)
... by equating it with a "metric space", ... Much of the motivation for point set topology comes from ... Note that the definition above actually says that the *distance* ... geodesics in string space. ... (sci.math)  Why Topology? (was irrationality 0.201201020100201000201...)
... by equating it with a "metric space", ... Much of the motivation for point set topology comes from ... Note that the definition above actually says that the *distance* ... geodesics in string space. ... (sci.cognitive)  Why Topology? (was irrationality 0.201201020100201000201...)
... by equating it with a "metric space", ... Much of the motivation for point set topology comes from ... Note that the definition above actually says that the *distance* ... geodesics in string space. ... (sci.physics)  Re: quantum spaces
... David Macmanus wrote: ... > A space is complete if every Cauchy sequence of vectors converges to a ... complete metric space), then they are the same thing. ... metric space such as a normed space or an inner product space. ... (sci.physics) 
