ONT Re: Manifolds Of Sensuous Impressions (MOSI's)
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| Well now, can our little feeling, thus left alone in the universe, --
| for the god and we psychological critics may be supposed left out
| of the account, -- can the feeling, I say, be said to have any sort
| of a cognitive function? For it to 'know', there must be something
| to be known. What is there, on the present supposition?
| One may reply, "the feeling's content 'q'."
|
| William James, 'The Meaning of Truth',
| Longmans, Green, & Co., London, 1909,
| page 5.
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| It is also convenient to have a local terminology.
| Let U be an open set (of a manifold or a Banach space)
| containing a point x_0. By a "local isomorphism" at x_0
| we mean an isomorphism
|
| f : U_1 -> V
|
| from some open set U_1 containing x_0 (and contained in U)
| to an open set V (in some manifold or some Banach space).
| Thus a local isomorphism is essentially a change of chart,
| locally near a given point.
|
| Lang, DARM, page 23.
|
| Serge Lang,
|'Differential & Riemannian Manifolds',
| Springer-Verlag, New York, NY, 1995.
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
References And Incidental Nuances (RAIN)
http://www.philosophy.ru/library/kant/01/cr_pure_reason.html
http://ez2www.com/go.php3?site=book&go=0387943382
http://hallmathematics.com/mathematics/1433.shtml
http://hallmathematics.com/mathematics/630.shtml
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤