A laterally commutative heap can be defined on a given set iff there is the structure of a TST-space on this set.
@article{urn:eudml:doc:38989, title = {Laterally commutative heaps and TST-spaces.}, journal = {Stochastica}, volume = {11}, year = {1987}, pages = {229-233}, zbl = {0674.20045}, mrnumber = {MR0990886}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38989} }
Volenec, Vladimir. Laterally commutative heaps and TST-spaces.. Stochastica, Tome 11 (1987) pp. 229-233. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38989/