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Loop (topology)

Index Loop (topology)

A loop in mathematics, in a topological space X is a continuous function f from the unit interval I. [1]

15 relations: Continuous function, Free loop, Fundamental group, Loop algebra, Loop group, Loop space, Mathematics, Path (topology), Pointed space, Princeton University Press, Quasigroup, Quotient space (topology), Topological space, Unit circle, Unit interval.

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.

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Free loop

In the mathematical field of topology, a free loop is a variant of the mathematical notion of a loop.

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Fundamental group

In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

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Loop algebra

In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics.

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Loop group

In mathematics, a loop group is a group of loops in a topological group G with multiplication defined pointwise.

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Loop space

In topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of (based) loops in X, maps from the circle S1 to X, equipped with the compact-open topology.

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

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Path (topology)

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

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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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Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

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In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible.

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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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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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Unit circle

In mathematics, a unit circle is a circle with a radius of one.

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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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[1] https://en.wikipedia.org/wiki/Loop_(topology)

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