An image suitable for a skyscraper sheaf?

Question

This question relates to this thread:

Skyscraper sheaf?

Consider one of the diagramms for the representation of a sheaf (and stalks thereof) which are popular on the web:

I just wanted to know whether the representation on each point represents a closed or an open point and whether it is in fact the representation of a skyscraper sheaf.

Thanks in adavance.

Answer 1

This does not depict a skyscraper sheaf. As explained in the description here, it represents a sheaf over a discrete space $X=\{r,g\}$, i.e. where both points are open and closed at the same time. A section over the open set $\{r\}$ corresponds to a choice of a red point, and a section over the open set $\{g\}$ corresponds to a choice of a green point.