Sentences with TOPOLOGICAL-SPACE
Check out our example sentences below to help you understand the context.Sentences
1
"A topological space is a set together with a collection of open sets."
2
"In mathematics, a topological space may also be called a topo-space or a topological set."
3
"The concept of a topological space is important in the field of topology."
4
"A topological space can be finite or infinite."
5
"The properties of a topological space depend on the collection of open sets defined on it."
6
"A closed set in a topological space is defined as the complement of an open set."
7
"In a topological space, the union of any collection of open sets is also an open set."
8
"The intersection of finitely many open sets in a topological space is again an open set."
9
"A topological space is said to be connected if it cannot be partitioned into two disjoint open sets."
10
"The set of real numbers with the usual topology forms a topological space."
11
"A topological space is Hausdorff if for any two distinct points, there exist disjoint neighborhoods around them."
12
"The product of two topological spaces is itself a topological space."
13
"A compact topological space is one where every open cover has a finite subcover."
14
"A topological space is said to be complete if every Cauchy sequence converges in that space."
15
"In computer science, topological spaces are used in algorithms for data clustering."
16
"The concept of topological spaces generalizes the notion of distance in metric spaces."
17
"In topology, the concept of continuity plays a central role in defining topological spaces."
18
"A topological space is said to be separable if it contains a countable dense subset."
19
"The notion of convergence can be defined in a topological space."
20
"The study of topological spaces is an important area in mathematics."
1
"A topological space is a set together with a collection of open subsets."
2
"In mathematics, a topological space is a fundamental concept in topology."
3
"The notion of a topological space is used to define what it means for a set to be 'closely mapped' to another set."
4
"In the study of topological spaces, continuity is a key property."
5
"A topological space is said to be Hausdorff if any two distinct points have disjoint neighbourhoods."
6
"The concept of connectedness is an important property of a topological space."
7
"In topology, a homeomorphism is an isomorphism between two topological spaces."
8
"A metric space is an example of a topological space."
9
"The concept of a topological space generalizes the notions of distance and continuity."
