Recall that two spaces X and Y are called topologically equivalent,or homeomorphic, if there is a bijection (one-to-one correspondence) f : X → Y that is continuous and whose inverse f −1 : Y → X is also continuous. Such a map is called a homeomorphism between X and Y. Intuitively, two spaces are homeomorphic if they can be mapped to one another without either tearing or gluing (imagine the objects are made of some elastic material).
Unable to display preview. Download preview PDF.