Open set (differential equation)

  • Thread starter stanley.st
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  • #1
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Main Question or Discussion Point

Hello !

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

[tex]x'=f(t,x)\,;\;f:\Omega\subset\mathbb{R}\times\mathbb{R}\to\mathbb{R}[/tex]

Omega is open. Why Omega must be open? Thanks
 

Answers and Replies

  • #2
mathman
Science Advisor
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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.
 

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