Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Install
Faster access than browser!
 

Topologist's sine curve

+ Save concept

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. [1]

18 relations: Compact space, Connected space, Counterexamples in Topology, Dover Publications, Graph of a function, Heine–Borel theorem, Interval (mathematics), Lebesgue covering dimension, Limit point, Locally compact space, Locally connected space, Mathematics, Path (topology), Shape theory (mathematics), Subspace topology, Topological space, Topology, Two-dimensional space.

Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

New!!: Topologist's sine curve and Christmas · See more »

Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

New!!: Topologist's sine curve and Christmas and holiday season · See more »

Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

New!!: Topologist's sine curve and Christmas Eve · See more »

Christmas traditions

Christmas traditions vary from country to country.

New!!: Topologist's sine curve and Christmas traditions · See more »

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).

New!!: Topologist's sine curve and Compact space · See more »

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.

New!!: Topologist's sine curve and Connected space · See more »

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.

New!!: Topologist's sine curve and Counterexamples in Topology · 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.

New!!: Topologist's sine curve and Dover Publications · See more »

Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

New!!: Topologist's sine curve and Graph of a function · See more »

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.

New!!: Topologist's sine curve and Heine–Borel theorem · See more »

Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

New!!: Topologist's sine curve and Interval (mathematics) · See more »

Lebesgue covering dimension

In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically invariant way.

New!!: Topologist's sine curve and Lebesgue covering dimension · See more »

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.

New!!: Topologist's sine curve and Limit point · See more »

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.

New!!: Topologist's sine curve and Locally compact space · See more »

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.

New!!: Topologist's sine curve and Locally connected space · See more »

Mathematics

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

New!!: Topologist's sine curve and Mathematics · See more »

New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

New!!: Topologist's sine curve and New Year · See more »

New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

New!!: Topologist's sine curve and New Year's Day · See more »

New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

New!!: Topologist's sine curve and New Year's Eve · See more »

Path (topology)

In mathematics, a path in a topological space X is a continuous function f from the unit interval I.

New!!: Topologist's sine curve and Path (topology) · See more »

Shape theory (mathematics)

Shape theory is a branch of topology, which provides a more global view of the topological spaces than homotopy theory.

New!!: Topologist's sine curve and Shape theory (mathematics) · See more »

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).

New!!: Topologist's sine curve and Subspace topology · See more »

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.

New!!: Topologist's sine curve and Topological space · See more »

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.

New!!: Topologist's sine curve and Topology · See more »

Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

New!!: Topologist's sine curve and Two-dimensional space · See more »

2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

New!!: Topologist's sine curve and 2018 · See more »

2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

New!!: Topologist's sine curve and 2019 · See more »

Redirects here:

Topologist sine curve, Y = sin(1/x), Y=sin(1/x).

References

[1] https://en.wikipedia.org/wiki/Topologist's_sine_curve

OutgoingIncoming
Hey! We are on Facebook now! »