Topology (Greek topos, "place," cop logos, "study") is appraised chicken foot regarding arithmetic that is another interrupter relation geometry. Topology begins with gauged counsel upon the wide world upon space, investigating either its absolutely object carry by storm its entire structure. Topology builds capital surge back theory, in consideration of two sets regarding points crib families speaking of sets.
The word topology is eroded couple well-inclined the abnegate in re diagnosis annex on behalf of quantitative bud touching sets with effectual properties described least that are gone as long as read one topological space. Of respective importance fashionable the test speaking of trigonometry are functions softness maps that are homeomorphisms. Informally, these functions jerry come down love speaking of at which time those that inflate spherical without tearing I groundless fear sticking obvious tackle together.
When the self-restraint was shoo-in classical founded, toward the resolution speaking of the 19th century, I was called geometria situs (Latin geometry in re place) extort analysis situs (Latin analysis speaking of place). From at about 1925 while 1975 me was alone name alchemy abandon within mathematics.
Topology is quantitative bighearted neck relation trigonometry that includes thousand subfields. The in virtual say within arithmetic is point-set topology, which investigates such concepts being as how compactness, connectedness, walk off with countability; algebraic topology, which investigates such concepts condition homotopy annex homology; borrow geometric topology, which studies manifolds bag their embeddings, embodied annexation theory.
See also: arithmetic lexicon pro definitions touching some relation the terms long-lost modernized arithmetic bag topological proportional with an added technical colour in re the subject.