Vipul: New page: ==Statement== Suppose $X$ is a normal space, $f:X \to [0,1]$ is an upper semicontinuous function and $g:X \to [0,1]$ is a lower semicontinuous functio...

2008-12-09T02:51:05Z

New page: ==Statement== Suppose <math>X</math> is a normal space, <math>f:X \to [0,1]</math> is an upper semicontinuous function and <math>g:X \to [0,1]</math> is a lower semicontinuous functio...

New page

==Statement==

Suppose <math>X</math> is a [[normal space]], <math>f:X \to [0,1]</math> is an upper semicontinuous function and <math>g:X \to [0,1]</math> is a lower semicontinuous function. Suppose further than <math>f \le g</math> pointwise. Then, there exists a continuous function <math>h:X \to [0,1]</math> such that <math>f \le h \le g</math>.

Conversely, if <math>X</math> is a topological space satisfying the above condition, then <math>X</math> is normal.

Hahn-Dieudonne-Tong insertion theorem - Revision history

Vipul: New page: ==Statement== Suppose X is a normal space, f:X \to [0,1] is an upper semicontinuous function and g:X \to [0,1] is a lower semicontinuous functio...

Vipul: New page: ==Statement== Suppose $X$ is a normal space, $f:X \to [0,1]$ is an upper semicontinuous function and $g:X \to [0,1]$ is a lower semicontinuous functio...