Open set (differential equation)

[stanley.st]

Hello !

When I'm reading something about differential equations everywhere it's about open sets. For example when we define special kind of equation

$$x'=f(t,x)\,;\;f:\Omega\subset\mathbb{R}\times\mathbb{R}\to\mathbb{R}$$

Omega is open. Why Omega must be open? Thanks

 

[mathman]

I don't know what is the full context. However even if Ω is not open, it must contain an open set for the diff. equ. to be meaningful.