Juh•sz [4] has summarized known results on the partial ordering of cardinal functions on orderable topological spaces and on arbitrary T 2 spaces. (All spaces in this paper are assumed to be T 2, unless noted otherwise.) Here we show this partial ordering on some classes satisfying weaker order conditions: suborderable spaces (= GO spaces), locally orderable spaces, and Frechet chain net spaces (see definitions below). With some exceptions (which are noted) our results are shown to be best possible. The outline of the paper is as follows: after an introductory section, there are three sections, each of which deals with the partial ordering of cardinal functions for a different class of spaces. Proofs are in Section 5 and examples in Section 6. The authors are grateful to I. Juhgsz and D. Perlis for helpful comments. Section 1. Notation and Terminology. With minor exceptions (which will be noted) we follow [4]; definitions not included here can be found there. If •0 is any cardinal function there is an associated function denoted by her •0, where her •0(X) = sup{•0Y: Y C X}. We often abbreviate the notation •0X to •0 if no confusion will result. The following cardinal functions are considered: w = weight L = Linde16f degree d = density c = cellularity (also called Suslin number) s = spread = her c h = height = her L z = width = her d