Given a sheaf of sets over a topological space , the section over an arbitrary (= not necessarily open) subset is a continuous section of the corresponding etale space restricted to .
A sheaf of sets (or of abelian groups) over a paracompact Hausdorff space is soft if for any closed subset , every section of over can be extended to the whole .
The local extension of germs to the open neighborhoods of points by paracompactness gives rise to an extension of the section to an open neighborhood of the whole set . Therefore every flabby sheaf is soft, because flabbiness gives the extension from open subsets. Fine sheaves are always soft.
soft sheaf
Standard references are Tohoku and
Last revised on April 1, 2019 at 10:01:32. See the history of this page for a list of all contributions to it.