Formal Definition
A topological space X is said to be locally regular if and only if each point, x, of X has a neighbourhood that is regular under the subspace topology. Equivalently, a space X is locally regular if and only if the collection of all open sets that are regular under the subspace topology forms a base for the topology on X.
Read more about this topic: Locally Regular Space
Famous quotes containing the words formal and/or definition:
“There must be a profound recognition that parents are the first teachers and that education begins before formal schooling and is deeply rooted in the values, traditions, and norms of family and culture.”
—Sara Lawrence Lightfoot (20th century)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)