Definition talk:Partition of Unity (Topology)

It's not too important whether the supports are open or closed. We want this condition so that the sum in the condition

$(3): \quad \ds \forall x \in X: \sum_{\alpha \mathop \in A} \map {\phi_\alpha} x = 1$

is defined. Therefore we may as well either take the supports to be open, or if supports are to be closed (the main convention I have seen) take the interior of the supports in condition $(1)$.

This way will also be more in keeping with the convention regarding the definition of a partition of unity subordinate to an open cover of $X$. --Linus44 (talk) 19:10, 15 September 2013 (UTC)

Care to contribute towards the page(s) in question (specifically those on "Support")? I'm not familiar with this area. --prime mover (talk) 19:16, 15 September 2013 (UTC)

Added a slightly more general than needed definition of support; the page'll get even messier if every possible permutation is added. --Linus44 (talk) 12:16, 17 September 2013 (UTC)

Makes good sense to me. The page is IMO not messy at all (except where there are templates for unfinished stuff). --prime mover (talk) 16:51, 17 September 2013 (UTC)