An intrinsic definition of topological equivalence (independent of any larger ambient space) involves a special type of function known as a homeomorphism. A function h is a homeomorphism, and objects X and Y are said to be homeomorphic, if and only if the function satisfies the following conditions. The notion of two objects being homeomorphic provides the definition of intrinsic topological equivalence and is the generally accepted meaning of topological equivalence. Two objects that are isotopic in some ambient space must also be homeomorphic. Thus, extrinsic topological equivalence implies intrinsic topological equivalence. In its most general setting, topology involves objects ...(100 of 2963 words)