User talk:Sniffnoy: Difference between revisions

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Topological definition of continous function

Dear Sniffnoy,

Motivation for modification of :

suppose we have a function $f:X\rightarrow Y$ , where X and Y are topological spaces.

To :

suppose we have a function f : X → Y between two topological spaces {X,T_X} and {Y,T_Y}.

was simply to clarify that the map f is defined between the sets X and Y, as opposed to only being defined between the topologies T_X and T_Y, which someone learning for the first time might mistakenly think.

e.g. see :

http://www.dpmms.cam.ac.uk/site2002/Teaching/IB/MetricTopologicalSpaces/2005-2006/L1topspaces.pdf

Thanks

@@ Line 66: / Line 66: @@
 |}
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+== Topological definition of continous function ==
+Dear Sniffnoy,
+Motivation for modification of :
+suppose we have a function <math>f:X\rightarrow Y</math>, where ''X'' and ''Y'' are topological spaces.
+To :
+suppose we have a function ''f'' : ''X'' &rarr; ''Y'' between two [[topological space]]s  {''X'',''T<sub>X</sub>''} and {''Y'',''T<sub>Y</sub>''}.
+was simply to clarify that the map f is defined between the sets ''X'' and ''Y'', as opposed to only being defined between the topologies ''T<sub>X</sub>'' and ''T<sub>Y</sub>'', which someone learning for the first time might mistakenly think.
+e.g. see :
+http://www.dpmms.cam.ac.uk/site2002/Teaching/IB/MetricTopologicalSpaces/2005-2006/L1topspaces.pdf
+Thanks