In mathematics, specifically algebraic topology, the phrase semi-locally simply connected refers to a certain local connectedness condition that arises in the theory of covering spaces. Roughly speaking, a topological space X is semi-locally simply connected if there is a lower bound on the sizes of the “holes” in X. This condition is necessary for most of the theory of covering spaces, including the existence of a universal cover and the Galois correspondence between covering spaces and subgroups of the fundamental group.
Most “nice” spaces such as manifolds and CW complexes are semi-locally simply connected, and topological spaces that do not satisfy this condition are considered somewhat pathological. The standard example of a non-semi-locally simply connected space is the Hawaiian earring.
Read more about Semi-locally Simply Connected: Definition, Examples, Topology of Fundamental Group
Famous quotes containing the words simply and/or connected:
““As for myself, I am simply Hop-Frog, the jester—and this is my last jest.”... The Work of vengeance was complete.”
—Edgar Allan Poe (1809–1849)
“Before I had my first child, I never really looked forward in anticipation to the future. As I watched my son grow and learn, I began to imagine the world this generation of children would live in. I thought of the children they would have, and of their children. I felt connected to life both before my time and beyond it. Children are our link to future generations that we will never see.”
—Louise Hart (20th century)