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35 relations: Algebraic topology, Allen Hatcher, Ball (mathematics), Category of topological spaces, Circle, Compact space, Comparison of topologies, Cone, Cone (disambiguation), Connected space, Contractible space, Cylinder, Desuspension, Disk (mathematics), Euclidean space, Functor, Hausdorff space, Homeomorphism, Homotopy, Join (topology), Mapping cone (topology), N-sphere, Point (geometry), Pointed space, Polygon, Product topology, Quotient space (topology), Simplex, Subspace topology, Suspension (topology), Topological space, Topology, Triangle, Union (set theory), Unit interval.
Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
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Allen Hatcher
Allen Edward Hatcher (born October 23, 1944) is an American topologist.
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Ball (mathematics)
In mathematics, a ball is the space bounded by a sphere.
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Category of topological spaces
In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps or some other variant; for example, objects are often assumed to be compactly generated.
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Circle
A circle is a simple closed shape.
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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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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.
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Cone
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
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Cone (disambiguation)
A cone is a basic geometrical shape.
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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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Contractible space
In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map.
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Cylinder
A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
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Desuspension
In topology, a field within mathematics, desuspension is an operation inverse to suspension.
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Disk (mathematics)
In geometry, a disk (also spelled disc).
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Functor
In mathematics, a functor is a map between categories.
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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.
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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.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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Join (topology)
In topology, a field of mathematics, the join of two topological spaces A and B, often denoted by A\ast B or A\star B, is defined to be the quotient space where I is the interval and R is the equivalence relation generated by At the endpoints, this collapses A\times B\times \ to A and A\times B\times \ to B. Intuitively, A\star B is formed by taking the disjoint union of the two spaces and attaching a line segment joining every point in A to every point in B.
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Mapping cone (topology)
In mathematics, especially homotopy theory, the mapping cone is a construction C_f of topology, analogous to a quotient space.
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N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
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Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
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Pointed space
In mathematics, a pointed space is a topological space with a distinguished point, the basepoint.
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Polygon
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
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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.
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Quotient space (topology)
In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space.
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Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
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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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Suspension (topology)
In topology, the suspension SX of a topological space X is the quotient space: of the product of X with the unit interval I.
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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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Triangle
A triangle is a polygon with three edges and three vertices.
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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Unit interval
In mathematics, the unit interval is the closed interval, that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1.
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References
[1] https://en.wikipedia.org/wiki/Cone_(topology)
