Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $D$ be a convex domain in the complex plane, and is domain $D$ a simply connected domain? What about when $D$ is a star domain?

share|improve this question

1 Answer 1

Yes star-domains are simply connected, since every path is homotopy equivalent to one going through the center.

The disc with one point removed is not simply connected, but also not convex.

Open convex sets are among the star-domains.

All that is not special to the $\mathbb{C}$, but any $\mathbb{R}^d$.

share|improve this answer
    
the disc with one point removed is not a convex domain! –  Riemann Apr 15 '12 at 13:09
    
The disc with one (interior) point removed is not convex, either, right? –  Gerry Myerson Apr 15 '12 at 13:09
    
You can check using the definition do convex domain!!! –  Riemann Apr 15 '12 at 13:12
    
Okay I missed the convex assumption;( Yes convex open sets are connected and simply connected. –  plusepsilon.de Apr 15 '12 at 13:13
    
@late_learner can you give me a proof? thank you! –  Riemann Apr 15 '12 at 13:15

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.