ABSTRACT
A summant on a figure K is just a function on the set of all tagged cells in K. So the summants on K form a Riesz space ¥ under the pointwise operations and ordering for real-valued functions on a set. In the Riesz space Y the summants S ~ 0 form a Riesz ideal Z. That is, Z is a linear subspace of Y such that for all S', T in Y
To verify that Z is a linear space we have for S, T belonging to Z, j ^ |S + r | < £ |S |+ 7 7 m = 0 and j£ |c S | = |c| j ^ |5 | = 0
I k ISI < J^ \T \. So / K|S| = 0 if f K \T\ = 0.
