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Locally connected space and Topologist's sine curve

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Locally connected space and Topologist's sine curve

Locally connected space vs. Topologist's sine curve

In topology and other branches of mathematics, a topological space X is locally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets. In the branch of mathematics known as topology, the topologist's sine curve or Warsaw sine curve is a topological space with several interesting properties that make it an important textbook example.

Similarities between Locally connected space and Topologist's sine curve

Locally connected space and Topologist's sine curve have 11 things in common (in Unionpedia): Compact space, Connected space, Counterexamples in Topology, Dover Publications, Heine–Borel theorem, Locally compact space, Locally connected space, Mathematics, Subspace topology, Topological space, Topology.

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).

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Connected space

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.

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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 Locally connected space · Counterexamples in Topology and Topologist's sine curve · See more »

Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.

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Heine–Borel theorem

In real analysis the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S of Euclidean space Rn, the following two statements are equivalent.

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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.

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Locally connected space

In topology and other branches of mathematics, a topological space X is locally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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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).

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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.

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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.

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The list above answers the following questions

Locally connected space and Topologist's sine curve Comparison

Locally connected space has 45 relations, while Topologist's sine curve has 18. As they have in common 11, the Jaccard index is 17.46% = 11 / (45 + 18).

References

This article shows the relationship between Locally connected space and Topologist's sine curve. To access each article from which the information was extracted, please visit:

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