Faster access than browser!Similarities between Compact space and Trivial topology
Compact space and Trivial topology have 25 things in common (in Unionpedia): Closed set, Continuous function, Counterexamples in Topology, Discrete space, Empty set, First-countable space, Hausdorff space, Homeomorphism, Limit point, Lindelöf space, Locally compact space, Open set, Order topology, Paracompact space, Product topology, Second-countable space, Separable space, Separation axiom, Sequence, Sequentially compact space, Singleton (mathematics), Subspace topology, Topological space, Tychonoff space, Uniform space.
Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
Closed set and Compact space · Closed set and Trivial topology ·
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.
Compact space and Continuous function · Continuous function and Trivial topology ·
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.
Compact space and Counterexamples in Topology · Counterexamples in Topology and Trivial topology ·
Discrete space
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense.
Compact space and Discrete space · Discrete space and Trivial topology ·
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.
Compact space and Empty set · Empty set and Trivial topology ·
First-countable space
In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability".
Compact space and First-countable space · First-countable space and Trivial topology ·
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.
Compact space and Hausdorff space · Hausdorff space and Trivial topology ·
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.
Compact space and Homeomorphism · Homeomorphism and Trivial topology ·
Limit point
In mathematics, a limit point (or cluster point or accumulation point) of a set S in a topological space X is a point x that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself.
Compact space and Limit point · Limit point and Trivial topology ·
Lindelöf space
In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover.
Compact space and Lindelöf space · Lindelöf space and Trivial topology ·
Locally compact space
In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.
Compact space and Locally compact space · Locally compact space and Trivial topology ·
Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
Compact space and Open set · Open set and Trivial topology ·
Order topology
In mathematics, an order topology is a certain topology that can be defined on any totally ordered set.
Compact space and Order topology · Order topology and Trivial topology ·
Paracompact space
In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite.
Compact space and Paracompact space · Paracompact space and Trivial topology ·
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.
Compact space and Product topology · Product topology and Trivial topology ·
Second-countable space
In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base.
Compact space and Second-countable space · Second-countable space and Trivial topology ·
Separable space
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.
Compact space and Separable space · Separable space and Trivial topology ·
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.
Compact space and Separation axiom · Separation axiom and Trivial topology ·
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
Compact space and Sequence · Sequence and Trivial topology ·
Sequentially compact space
In mathematics, a topological space is sequentially compact if every infinite sequence has a convergent subsequence.
Compact space and Sequentially compact space · Sequentially compact space and Trivial topology ·
Singleton (mathematics)
In mathematics, a singleton, also known as a unit set, is a set with exactly one element.
Compact space and Singleton (mathematics) · Singleton (mathematics) and Trivial topology ·
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).
Compact space and Subspace topology · Subspace topology and Trivial topology ·
Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
Compact space and Topological space · Topological space and Trivial topology ·
Tychonoff space
In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces.
Compact space and Tychonoff space · Trivial topology and Tychonoff space ·
Uniform space
In the mathematical field of topology, a uniform space is a set with a uniform structure.
Compact space and Uniform space · Trivial topology and Uniform space ·
The list above answers the following questions
- What Compact space and Trivial topology have in common
- What are the similarities between Compact space and Trivial topology
Compact space and Trivial topology Comparison
Compact space has 146 relations, while Trivial topology has 60. As they have in common 25, the Jaccard index is 12.14% = 25 / (146 + 60).
References
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