What does $S^1 \setminus \{{pt}\}$ mean?

Question

In this paper, expression $S^1 \setminus \{{pt}\}$ is used on page 6. The $\{{pt}\}$ is not definied there. What does it mean and is it a standard notation?

Answer 1

It just means the circle minus any point. They choose the notation $ \{pt\} $ because the specific point is irrelevant, so the author chose not to specify one.

Answer 2

Its $S^1$ with a point removed. $S^1$ is symmetric so the point can be chosen arbitrarily.

Answer 3

It is called as cut point for circle i.e removing one point from circle.