View source for Combinatorial topology

A branch of topology in which the topological properties of geometrical figures are studied by means of their divisions (cf. [[Division|Division]]) into more elementary figures (for example, the triangulation of polyhedra into simplexes) or by means of coverings (cf. [[Covering|Covering]]) by systems of sets. These methods are applied under the most general hypotheses concerning the figures being studied.

====Comments====
Around 1930, combinatorial topology was the name given to a fairly coherent area covering parts of general, algebraic and piecewise-linear (PL) topology. Typical subjects are: simplicial complexes, their fundamental groups and homology groups, surfaces, and topology of 3- or higher-dimensional manifolds (cf. [[Fundamental group]]; [[Homology group]]; [[Manifold]]; [[Simplicial complex]]; [[Surface]]). Most of these topics have nowadays developed to specialisms in most diverse branches of mathematics.

One of the classical textbooks (in German) has recently been translated to English; cf. [[#References|[a1]]].

====References====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top">  P.S. Aleksandrov,   "Combinatorial topology" , Graylock , Rochester  (1956)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  L.S. Pontryagin,   "Grundzüge der kombinatorischen Topologie" , Deutsch. Verlag Wissenschaft.  (1956)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  H. Seifert,   W. Threlfall,   "A textbook of topology" , Acad. Press  (1980)  (Translated from German)</TD></TR>
</table>