Curve selection lemma

There are many versions of the curve selection lemma.

In o-minimal structures, we have to consider definable curves, definable functions, deinable sets,… The definition of definable sets,… we can find in many documents.

Let fr(A) be frontier of A, ie fr(A) = \bar{A} - A . We have:

Curve selection lemma: In the o-minimal structure \mathcal{O}. If x \in fr(A), then there is a definable map \gamma: [0, 1) \to \mathbb{R}^n such that \gamma(0,1) \subset A and \gamma(0) = x .

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s