# sections over compact subsets extend to global?

Suppose S is a sheaf (of abelian groups, say) over a space X. Is there a name for the property: (*) every continuous section over a compact subset K of X extends to a global section? Note that X need not be T_2 etc.

If we replace "compact" by "closed" then we have a "soft" sheaf

If we replace "compact" by "open" we have a "flabby" sheaf

Is there a standard term used in the compact case?

Example: a sheaf over a 0-dimensional space has this property *, but is not necessarily fine or flabby.

-
If you replace "compact" by "closed", you obtain a "soft" sheaf, not a "fine" sheaf. ( Fine is a stronger notion: fine $\Rightarrow$ soft.) –  Georges Elencwajg Nov 17 '11 at 19:12
Thanks for the correction. Now fixed. –  Peter T Nov 18 '11 at 0:34