Faster access than browser!Similarities between Discrete space and Topological space
Discrete space and Topological space have 25 things in common (in Unionpedia): Base (topology), Category theory, Compact space, Comparison of topologies, Complete metric space, Continuous function, Counterexamples in Topology, Empty set, Finite set, Hausdorff space, Homeomorphism, Manifold, Mathematical structure, Metric space, Morphism, Neighbourhood (mathematics), Open set, Product topology, Separation axiom, Set (mathematics), Subset, Subspace topology, Topological group, Topology, Trivial topology.
Base (topology)
In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B.We are using a convention that the union of empty collection of sets is the empty set.
Base (topology) and Discrete space · Base (topology) and Topological space ·
Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
Category theory and Discrete space · Category theory and Topological space ·
Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
Compact space and Discrete space · Compact space and Topological space ·
Comparison of topologies
In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set.
Comparison of topologies and Discrete space · Comparison of topologies and Topological space ·
Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).
Complete metric space and Discrete space · Complete metric space and Topological space ·
Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
Continuous function and Discrete space · Continuous function and Topological space ·
Counterexamples in Topology
Counterexamples in Topology (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr. In the process of working on problems like the metrization problem, topologists (including Steen and Seebach) have defined a wide variety of topological properties.
Counterexamples in Topology and Discrete space · Counterexamples in Topology and Topological space ·
Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
Discrete space and Empty set · Empty set and Topological space ·
Finite set
In mathematics, a finite set is a set that has a finite number of elements.
Discrete space and Finite set · Finite set and Topological space ·
Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.
Discrete space and Hausdorff space · Hausdorff space and Topological space ·
Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
Discrete space and Homeomorphism · Homeomorphism and Topological space ·
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
Discrete space and Manifold · Manifold and Topological space ·
Mathematical structure
In mathematics, a structure on a set is an additional mathematical object that, in some manner, attaches (or relates) to that set to endow it with some additional meaning or significance.
Discrete space and Mathematical structure · Mathematical structure and Topological space ·
Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
Discrete space and Metric space · Metric space and Topological space ·
Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
Discrete space and Morphism · Morphism and Topological space ·
Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
Discrete space and Neighbourhood (mathematics) · Neighbourhood (mathematics) and Topological space ·
Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
Discrete space and Open set · Open set and Topological space ·
Product topology
In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.
Discrete space and Product topology · Product topology and Topological space ·
Separation axiom
In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider.
Discrete space and Separation axiom · Separation axiom and Topological space ·
Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
Discrete space and Set (mathematics) · Set (mathematics) and Topological space ·
Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
Discrete space and Subset · Subset and Topological space ·
Subspace topology
In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).
Discrete space and Subspace topology · Subspace topology and Topological space ·
Topological group
In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions with respect to the topology.
Discrete space and Topological group · Topological group and Topological space ·
Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
Discrete space and Topology · Topological space and Topology ·
Trivial topology
In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space.
Discrete space and Trivial topology · Topological space and Trivial topology ·
The list above answers the following questions
- What Discrete space and Topological space have in common
- What are the similarities between Discrete space and Topological space
Discrete space and Topological space Comparison
Discrete space has 68 relations, while Topological space has 141. As they have in common 25, the Jaccard index is 11.96% = 25 / (68 + 141).
References
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