demostrar que el conjunto {(x,yE R2/2x+y<1)}es abierto?

Answer 1

If A = { (x, y) | 2x + y < 1} in R^2,
and if (t, u) is in A,
then 2t + u < 1
and so 1 - (2t + u) > 0

Let r = ( 1 - (2t + u) ) / 3

The open ball with center (t, u) and radius r is completely contained in A so A is open.

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http://babelfish.altavista.com/

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"
Si A = {(x, y) | 2x + y 0 Deje r = (1 - (2t + u))/3 La bola abierta con el centro (t, u) y el radio r se contiene totalmente en A así que A está abierta.
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:-(