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:
“This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. It’s no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.”
—Leontine Young (20th century)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)