Topology may be roughly divided into point-set topology, which considers figures as sets of points having such properties as being open or closed, compact, connected, and so forth; combinatorial topology, which, in contrast to point-set topology, considers figures as combinations (complexes) of simple figures (simplexes) joined together in a regular manner; and algebraic topology, which makes extensive use of algebraic methods, particularly those of group theory. There is considerable overlap among these branches.
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.