Sentences with ULTRAFILTER
Check out our example sentences below to help you understand the context.Sentences
1
"An ultrafilter is a special kind of filter on a set."
2
"In mathematics, ultrafilters have applications in various branches such as topology and set theory."
3
"An ultrafilter is said to be non-principal if it does not contain any singletons."
4
"If X is a set and F is an ultrafilter on X, then either F or the complement of F is a filter."
5
"Given any set X, there exists an ultrafilter on X. This is a consequence of Zorn's lemma."
6
"Some properties of an ultrafilter F on a set X include: F does not contain the empty set, F is closed under supersets, and F is maximal with respect to those properties."
7
"The quotient space created by an ultrafilter on a set X is minimal among all topological quotients of X."
8
"The study of ultrafilters has deep connections with abstract algebra and logic."
9
"Ultrafilters can help define the concepts of ultrafilter convergence and ultraproducts."
10
"The existence of non-principal ultrafilters cannot be proved in Zermelo–Fraenkel set theory without the aid of additional axioms."
11
"The usage of ultrafilters in algebraic number theory allows the extension of some properties like primes and factorization to a larger context."
12
"Filters and ultrafilters play a significant role in the theory of Boolean algebras."
13
"The notion of an ultrafilter has applications beyond mathematics, such as in computer science and philosophy."
1
"An ultrafilter is a specific type of filter in mathematics."
2
"In topology, an ultrafilter is a particular kind of filter on a set."
3
"An ultrafilter on a set is a collection of subsets with certain properties."
4
"In mathematical logic, an ultrafilter is an important concept in model theory."
5
"An ultrafilter can be thought of as a maximal way to select elements from a set."
6
"The existence of nonprincipal ultrafilters is a consequence of the axiom of choice."
