A homology class in a singular homology theory is represented by a finite linear combination of geometric subobjects with zero boundary. Such a linear combination is considered to be homologous to zero if it is the boundary of something having dimension one greater. For instance, two points that can be connected by a path comprise the boundary for that path, so any two points in a component are homologous and represent the same homology class.
Homology Class
See also
Cohomology, Cohomology Class, Homology, Homology Group, Homology IntersectionThis entry contributed by Todd Rowland
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Rowland, Todd. "Homology Class." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HomologyClass.html