What does analysis situs mean?
Definitions for analysis situs
ana·ly·sis si·tus
This dictionary definitions page includes all the possible meanings, example usage and translations of the word analysis situs.
Princeton's WordNet
topology, analysis situsnoun
the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions
Wiktionary
analysis situsnoun
topology
ChatGPT
analysis situs
Analysis Situs, also known as Topology, is a branch of mathematics that deals with the properties of space that are preserved under continuous transformations, like stretching and bending. This includes concepts such as continuity, compactness, connectedness, convergence, and continuity. It is a way to study geometric figures and spaces at a deeper, more abstract level, beyond just their shape and size. Analysis situs is often described as "rubber-sheet geometry," because topologists consider figures that are equivalent if they can be deformed into each other without tearing or gluing.
Wikidata
Analysis Situs
Analysis Situs is the title of an influential mathematical paper, together with a series of five "Compléments", written by Henri Poincaré between 1895 and 1904. Besides providing the first systematic treatment of topology, Poincaré revolutionized the subject by using algebraic structures to distinguish between non-homeomorphic topological spaces, effectively creating the subject of algebraic topology. In the papers he introduced the concepts of fundamental group and simplicial homology, provided an early formulation of Poincaré duality, gave the Euler–Poincaré characteristic for chain complexes, and mentioned several important conjectures including the Poincaré conjecture.
Matched Categories
Numerology
Chaldean Numerology
The numerical value of analysis situs in Chaldean Numerology is: 8
Pythagorean Numerology
The numerical value of analysis situs in Pythagorean Numerology is: 8
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"analysis situs." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/analysis+situs>.
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