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The term "homology" was first used in biology by the anatomist Richard Owen in 1843 when studying the similarities of vertebrate fins and limbs, defining it as the "same organ in different animals under every variety of form and function", [6] and contrasting it with the matching term "analogy" which he used to describe different structures ...
Lastly, since there are many homology theories for topological spaces that produce the same answer, one also often speaks of the homology of a topological space. (This latter notion of homology admits more intuitive descriptions for 1- or 2-dimensional topological spaces, and is sometimes referenced in popular mathematics .)
Sequence homology is the biological homology between DNA, RNA, or protein sequences, defined in terms of shared ancestry in the evolutionary history of life. Two segments of DNA can have shared ancestry because of three phenomena: either a speciation event (orthologs), or a duplication event (paralogs), or else a horizontal (or lateral) gene ...
A simple type of analogy is one that is based on shared properties; [1] [2] and analogizing is the process of representing information about a particular subject (the analogue or source system) by another particular subject (the target system), [3] in order "to illustrate some particular aspect (or clarify selected attributes) of the primary domain".
1843, distinction between homology and analogy (the latter now referred to as homoplasy), Richard Owen, precursor concept. Homology is the term used to characterize the similarity of features that can be parsimoniously explained by common ancestry.
The generalization to situations in which both index and coindex are infinite, but the relative index of any pair of critical points is finite, is known as Floer homology. Sergei Novikov generalized this construction to a homology theory associated to a closed one-form on a manifold. Morse homology is a special case for the one-form df.
Homology (anthropology), analogy between human beliefs, practices or artifacts owing to genetic or historical connections; Homology (psychology), behavioral characteristics that have common origins in either evolution or development
In mathematics, a homology theory in algebraic topology is compactly supported if, in every degree n, the relative homology group H n (X, A) of every pair of spaces (X, A)is naturally isomorphic to the direct limit of the nth relative homology groups of pairs (Y, B), where Y varies over compact subspaces of X and B varies over compact subspaces of A.