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:
“Good artists exist simply in what they make, and consequently are perfectly uninteresting in what they are. A really great poet is the most unpoetical of all creatures. But inferior poets are absolutely fascinating. The worse their rhymes are, the more picturesque they look. The mere fact of having published a book of second-rate sonnets makes a man quite irresistible. He lives the poetry that he cannot write. The others write the poetry that they dare not realise.”
—Oscar Wilde (1854–1900)
“A peasant becomes fond of his pig and is glad to salt away its pork. What is significant, and is so difficult for the urban stranger to understand, is that the two statements are connected by an and and not by a but.”
—John Berger (b. 1926)