Disjoint sum of partially ordered sets
From Encyclopedia of Mathematics
disjoint sum of posets
Let 
and 
be two partially ordered sets (cf. Partially ordered set).
The disjoint sum 
of 
and 
is the disjoint union of the sets 
and 
with the original ordering on 
and 
and no other comparable pairs. A poset is disconnected if it is (isomorphic to) the disjoint sum of two sub-posets. Otherwise it is connected. The maximal connected sub-posets are called components.
The disjoint sum is the direct sum in the category of posets and order-preserving mappings. The direct product in this category is the Cartesian product 
with partial ordering
 |
References
| [a1] | W.T. Trotter, "Partially ordered sets" R.L. Graham (ed.) M. Grötschel (ed.) L. Lovász (ed.) , Handbook of Combinatorics , I , North-Holland (1995) pp. 433–480 |
How to Cite This Entry:
Disjoint sum of partially ordered sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Disjoint_sum_of_partially_ordered_sets&oldid=31701
Disjoint sum of partially ordered sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Disjoint_sum_of_partially_ordered_sets&oldid=31701
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article