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

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

## 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 ·

## 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 ·

## 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 ·

## Graph of a function

In mathematics, the graph of a function f is the collection of all ordered pairs.

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

## Heine–Borel theorem

In the topology of metric spaces 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 ·

## 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 ·

## Limit point

In mathematics, a limit point of a set S in a topological space X is a point x (which is in X, but not necessarily in S) 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 ·

## 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 ·

## 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 ·

## Mathematics

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

New!!: Topologist's sine curve and Mathematics ·

## 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) ·

## 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 ·

## 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, that satisfy a set of axioms relating points and neighbourhoods.

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

## Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study), is the study of topological spaces.

New!!: Topologist's sine curve and Topology ·

## Two-dimensional space

In physics and mathematics, two-dimensional space or bi-dimensional space is a geometric model of the planar projection of the physical universe.

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

## Redirects here:

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