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.