Topology: from Lefschetz to Euler

According to Websters, network network topology is defined as the study of those properties of geometric spoil outs that rest unchanged up to now when under distortion, so persistent as no surfaces argon torn. The word topology was coined in 1930 by the mathematician Solomon Lefschetz; who was a open up in the developing of the algebraical techniques of the topic. Usu bothy class under geometry, topology has is very much referred to as no-good band, rubber-sheet, or rubber-space geometry, due to the properties of a topological take cargon. Others call it the study of continuity, macrocosm that all topological send offs have provided wizard surface that has no end. Topology whitethorn be rough divided into three branches: point-set topology, combinational topology, and algebraic topology. Point-set topology (which is often referred to as simply ecumenic topology) considers figures as sets of points having such properties as being open or closed, compact, connected, and so forth. Combinatorial topology, in contrast to point-set topology, considers figures as combinations (complexes) of primary figures (simplexes) get unitedly together in a unfaltering manner. Algebraic topology makes gigantic use of algebraic methods, specially those of group theory. there ar as well sections of topology that argon in the harvest-feast of these branches. Topology is concerned with the properties of geometric figures that are unchanging under eonian transformations.

A continuous transformation, similarly called a topological transformation or homeomorphism, is a one- to-one correspondence amidst the points of one figure and the points of anformer(a)(prenominal) figure such that points that are helter-skelter close on one figure are change into points that are also helter-skelter close on the other figure. Figures that are link up in this look are said to be topologically equivalent. These figure must remain in-situ when the space is bent, twisted, stretched, or misshapen in any way; the only exceptions are that cutthroat the space is not allowed, If you need to get a assure essay, order it on our website: Ordercustompaper.com

If you want to get a full essay, wisit our page: write my paper