biextensional collapse

If 𝒞=(𝒜,r,𝒳) is a Chu spaceMathworldPlanetmath, we can define the biextensional collapse of 𝒞 to be (r^[A],r,rˇ[X]) where r(r^(a),rˇ(x))=r(a,x).

That is, to name the rows of the biextensional collapse, we just use functions representing the actual rows of the original Chu space (and similarly for the columns). The effect is to merge indistinguishable rows and columns.

We say that two Chu spaces are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath if their biextensional collapses are isomorphic.

Title biextensional collapse
Canonical name BiextensionalCollapse
Date of creation 2013-03-22 13:04:54
Last modified on 2013-03-22 13:04:54
Owner Henry (455)
Last modified by Henry (455)
Numerical id 6
Author Henry (455)
Entry type Definition
Classification msc 03G99
Defines equivalent Chu space