In mathematics, a monotonically normal space is a particular kind of normal space, with some special characteristics, and is such that it is hereditarily normal, and any two separated subsets are strongly separated. They are defined in terms of a monotone normality operator.
A topological space is said to be monotonically normal if the following condition holds:
For every, where G is open, there is an open set such that
- if then either or .
There are some equivalent criteria of monotone normality.
Read more about Monotonically Normal Space: Properties, Some Discussion Links
Famous quotes containing the words normal and/or space:
“You have promise, Mlle. Dubois, but you must choose between an operatic career and what is usually called “a normal life.” Though why it is so called is beyond me.”
—Eric Taylor, Leroux, and Arthur Lubin. M. Villeneuve (Frank Puglia)
“No being exists or can exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an effect arising from the first existence of being, because when any being is postulated, space is postulated.”
—Isaac Newton (1642–1727)