Examples of 'topological space' in a sentence
Meaning of "topological space"
topological space: A mathematical concept that defines a set of points along with a collection of open sets that satisfy specific criteria related to continuity and convergence
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- An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets); (loosely) the set X.
- An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets);
- the set X.
How to use "topological space" in a sentence
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topological space
Suppose is a topological space and is an equivalence relation on.
Every metric space is also a topological space.
A curve is a topological space which is locally homeomorphic to a line.
Every uniform space is also a topological space.
A topological space that is not resolvable is termed irresolvable.
Thus we use a category to generalize a topological space.
An irreducible component of a topological space is a maximal irreducible subset.
Every uniformizable space is a completely regular topological space.
Every separable topological space is ccc.
The focus here is on standard proximity on a topological space.
It can be any topological space at all.
A pseudomanifold is a special type of topological space.
Every countable topological space is separable.
To each metrical space can be associated a topological space.
This is how a topological space is defined.
See also
Properties of closed sets in a topological space.
This topological space is not considered a subspace of another space.
A real space is a defined to be a topological space with an involution.
A topological space without a complete.
A finite collection of subsets of a topological space is locally finite.
The relation of being homotopic is an equivalence relation on paths in a topological space.
One can compose paths in a topological space in an obvious manner.
Neighbourhood is also one of the basic concepts in a topological space.
The set of open subsets of a topological space determines a lattice.
A topological space in which the points are functions is called a function space.
The definition of an abstract topological space.
One topological space can carry many different orbifold structures.
Obviously every finite subset of a topological space is compact.
A topological space whose topology can be described by a metric is called metrizable.
This defines a topological space.
A topological space is separable exactly when there is a dense sequence of points.
Locally compact topological space.
A topological space is submaximal if and only if every dense subset is open.
It is compact if it is compact as a topological space.
This is a topological space.
A metric space is now considered a special case of a general topological space.
Real numbers form a topological space and a complete metric space.
Every real or complex affine or projective space is also a topological space.
Density of a topological space.
This term is often used to refer to elements of the topological space.
Hausdorff topological space.
A topological space is called resolvable if it is the union of two disjoint dense subsets.
Connected set in a topological space.
A topological space is irreducible if it is not the union of two proper closed subsets.
The dimension of a topological space.
A topological space that is the polytope of a finite simplicial complex is called a polyhedron.
The formal definition says that a topological space is compact if.
Any topological space which deformation retracts to a point is contractible and vice versa.
Bicontinuous topological space.
This holds even if the reals are replaced by a more general topological space.
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