Topology/Subspaces

Topology Subspaces Sequences Order Put simply, a subspace is analogous to a subset of a topological space. Subspaces have powerful applications in topology. Definition Let be a topological space, and let be a subset of . Define the open sets as follows: A set is open in if there exists a a set such that An important idea to note from the above definitions is that a set not being open or closed does not prevent it from being open or closed within a subspace. For example, as a subspace of itself is both open and closed. Topology Subspaces Sequences Order Topology