Definify.com

Webster 1913 Edition

Homology

Ho-mol′o-gy

,
Noun.
[Gr. [GREEK] agreement. See
Homologous
.]
1.
The quality of being homologous; correspondence; relation;
as, the
homology
of similar polygons
.
2.
(Biol.)
Correspondence or relation in type of structure in contradistinction to similarity of function; as, the relation in structure between the leg and arm of a man; or that between the arm of a man, the fore leg of a horse, the wing of a bird, and the fin of a fish, all these organs being modifications of one type of structure.
☞ Homology indicates genetic relationship, and according to Haeckel special homology should be defined in terms of identity of embryonic origin. See
Homotypy
, and
Homogeny
.
3.
(Chem.)
The correspondence or resemblance of substances belonging to the same type or series; a similarity of composition varying by a small, regular difference, and usually attended by a regular variation in physical properties;
as, there is an
homology
between methane,
CH4
, ethane,
C2H6
, propane,
C3H8
, etc.
, all members of the paraffin series. In an extended sense, the term is applied to the relation between chemical elements of the same group;
as, chlorine, bromine, and iodine are said to be in
homology
with each other
. Cf.
Heterology
.
General homology
(Biol.)
,
the higher relation which a series of parts, or a single part, bears to the fundamental or general type on which the group is constituted.
Owen.
–
Serial homology
(Biol.)
,
representative or repetitive relation in the segments of the same organism, – as in the lobster, where the parts follow each other in a straight line or series.
Owen.
See
Homotypy
. –
Special homology
(Biol.)
,
the correspondence of a part or organ with those of a different animal, as determined by relative position and connection.
Owen.

Definition 2024

homology

homology

English

Noun

homology ‎(plural homologies)

  1. A homologous relationship.
  2. (biology) A correspondence of structures in two life forms with a common evolutionary origin, such as flippers and hands.
  3. (chemistry) The relationship between the elements in the same group of the periodic table, or between organic compounds in a homologous series.
  4. (topology) A theory associating a system of groups to each topological space.
  5. (algebra) A certain system of groups associated to a chain complex.
  6. (genetics) The presence of the same series of bases in related genes.

Usage notes

  • Like many terms that start with a non-silent h but have emphasis on their second syllable, some people precede homology with an, others with a.
  • (biology): For a discussion of the use of the term homology (and by association homologous) in biology, see: Patterson, Colin. "Homology in Classical and Molecular Biology." Molecular Biology and Evolution 5, no. 6 (November 1988): 603–625. http://mbe.oxfordjournals.org/cgi/reprint/5/6/603.pdf (accessed 18 December 2009; archived 18 December 2009, http://www.webcitation.org/5m7rn4rCe )
  • (mathematics): When used attributively before the name of a topological space, as in homology n-sphere or homology manifold, the reference is to a space whose homology is the same as that of the space mentioned: an homology manifold, for example, is a space whose homology is that of some manifold.
  • (mathematics): In modern usage, the term is used to mean homology group. Thus, X did Y by computing the homology of Z means X did Y by computing the homology groups of Z. More loosely, as used in homology in a space, the term corresponds to a singular homology group (group of singular homologies).[1]

Derived terms

Related terms

Translations

See also

References

  1. 1 2 Homology on Wolfram MathWorld

Etymology

From homo- +‎ -logy.

In mathematics, the term was first used in a topological sense by French polymath Henri Poincaré, in a sense close to what is now called a bordism. Thus, he thought of a homology as a relation between manifolds mapped into a reference manifold. Such manifolds form a homology when they form the boundary of a higher-dimensional manifold inside the reference manifold. Poincaré simplified his definition by considering only spaces that were simplicial complexes (that had a triangulation), and only objects in the space made up of simplices in the triangulation. Eventually, Poincaré's version was replaced by the more general singular homology, which is what mathematicians mean by homology.

In modern usage, the term homology often means homology group. Thus, X did Y by computing the homology of Z means X did Y by computing the homology groups of Z. More loosely, as used in homology in a space, the term corresponds to a singular homology group (group of singular homologies).[1]


Similar Results