Homology (mathematics) - Wikipedia
网页In mathematics, the term homology [a], originally introduced in algebraic topology, has three primary, closely-related usages. The most direct usage of the term is to take the homology of a chain complex, resulting in a sequence of …
Homology | Morphology, Comparative Anatomy & Genetics
网页2024年8月31日 · Homology, in biology, similarity of the structure, physiology, or development of different species of organisms based upon their descent from a common evolutionary ancestor. Homology is contrasted with analogy, which is a functional similarity of structure based not upon common evolutionary origins.
Homology Definition & Meaning - Merriam-Webster
网页The similarity of a structure or function of parts of different origins based on their descent from a common evolutionary ancestor is homology. Analogy, by contrast, is a functional …
Homology (biology) - Wikipedia
网页The principle of homology: The biological relationships (shown by colours) of the bones in the forelimbs of vertebrates were used by Charles Darwin as an argument in favor of evolution. In biology, homology is similarity due to shared ancestry between a pair of structures or genes in different taxa.
Homology | Algebraic Topology, Geometric Structures
网页Homology, in mathematics, a basic notion of algebraic topology. Intuitively, two curves in a plane or other two-dimensional surface are homologous if together they bound a region—thereby distinguishing between an inside and an outside.
Homology - Definition and Examples - Biology Online Dictionary
网页2023年7月14日 · In biology, homology refers to the similarity of the structure, physiology, or development of various species of other organisms as a result of their shared evolutionary parent. It plays a huge part in evolutionary biology.
Homology -- from Wolfram MathWorld
网页2024年8月22日 · The homology of a space is an algebraic object which reflects the topology. The algebraic tools used are called homological algebra, and in that language, the homology is a derived functor, the homology of a long exact sequence.
网页This paper explores the basic ideas of simplicial structures that lead to simplicial homology theory, and introduces singular homology in order to demonstrate the equivalence of homology groups of homeomorphic topological spaces.
Homological algebra - Wikipedia
网页Homological algebra is the study of homological functors and the intricate algebraic structures that they entail; its development was closely intertwined with the emergence of category theory. A central concept is that of chain complexes, which can be studied through their homology and cohomology.
Introduction to Homology - SpringerLink
网页2021年6月19日 · Instead, we must return to the land of triangulations and dig more deeply, in order to define a family of topological invariants known as the homology groups. The basic idea of homology is to count n -dimensional holes.
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