Composant
Encyclopedia
In point-set topology, the composant of a point p in a continuum A is the union
of all proper subcontinua of A that contain p. If a continuum is indecomposable
, then its composants are pairwise disjoint. The composants of a continuum are dense
in that continuum.
Union (set theory)
In set theory, the union of a collection of sets is the set of all distinct elements in the collection. The union of a collection of sets S_1, S_2, S_3, \dots , S_n\,\! gives a set S_1 \cup S_2 \cup S_3 \cup \dots \cup S_n.- Definition :...
of all proper subcontinua of A that contain p. If a continuum is indecomposable
Indecomposable continuum
In point-set topology, an indecomposable continuum is a continuum that is not the union of any two of its proper subcontinua. The pseudo-arc is an example of a hereditarily indecomposable continuum. L. E. J...
, then its composants are pairwise disjoint. The composants of a continuum are dense
Dense set
In topology and related areas of mathematics, a subset A of a topological space X is called dense if any point x in X belongs to A or is a limit point of A...
in that continuum.