Topology is the geometry of distortion. It deals with fundamental geometric properties that are unaffected when we stretch, twist or otherwise change an object's size and shape. It studies lirear figures, surfaces or solids; anything from pretzels and knots to networks and maps. Another name for topology agalysis of postion the gcomerie of Euelid, Lubachevsky, Remann and others, which measure lengths and angles and are therefore called metric, topology is nonmetric and nonquantitative geometry. Its propositions hold as well for objects made of rubber as for the rigid figures encountered in metric geometry.
Topology seems a queer subiect; it delve into strangs implausible shapes and its propositions are either childishly obvious (that is, until you try to prove them) or so difficult and abstract that not even a topologist can explain their intuitive meaning. But topology is no queerer than the physical world as we now interpret it. A world made up entirely of erratic electrical gyrations in curved space requires a bizarre mathematics to do it justice. Euclidian geometry despite its familiar appearance, is a little too bizarre for this world; it is concerned with wholly fictitious objects-perfectly rigid figures and bodies which suffer no change when moved about. Topology starts from the sound premise that there are no rigid objects, that everything in the world is a little askew, and is further deformed when its position is altered. The aim is to find the elements of order in this disorder, the permanence in this impermanence.
回答第⑤空
【正确答案】：⑤inetric