| Line 23: | Line 23: | ||
(3) Finally, what can be said about <math> f(x_0)\,</math> | (3) Finally, what can be said about <math> f(x_0)\,</math> | ||
| − | and <math> g(y_0)\, </math> for any | + | and <math> g(y_0)\, </math> for any <math>x_0\in X </math> and <math>y_0 \in Y</math>? |
Revision as of 09:08, 9 February 2010
To ask a new question, add a line and type in your question. You can use LaTeX to type math. Here is a link to a short LaTeX tutorial.
To answer a question, open the page for editing and start typing below the question...
go back to the Discussion Page
I am having trouble with exercise 2.4.10. I don't understand how I can prove what is being asked without using a specific range or function. Can anyone help with this?
Prof. Alekseenko: Perhaps one could start from looking at functions $ f(x)\, $ and $ g(y)\, $ closely.
Here is a hint: consider any point $ (x_0,y_0) \, $.
(1) What can be said about $ f(x_{0})\, $ and $ h(x_0,y_0) \, $?
(2) Similarly, what can be said about $ g(y_{0})\, $ and $ h(x_0,y_0)\, $?
(3) Finally, what can be said about $ f(x_0)\, $
and $ g(y_0)\, $ for any $ x_0\in X $ and $ y_0 \in Y $?
(4) How can this help to establish the desired inequality?
Can anybody fill in the detail?
