Table of Contents
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 such that a small variation of the argument induces a small variation of the value of the function.
See Loop (topology) and Continuous function
Free loop
In the mathematical field of topology, a free loop is a variant of the notion of a loop. Loop (topology) and free loop are topology and topology stubs.
See Loop (topology) and Free loop
Fundamental group
In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space.
See Loop (topology) and Fundamental group
Loop algebra
In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics.
See Loop (topology) and Loop algebra
Loop group
In mathematics, a loop group (not to be confused with a loop) is a group of loops in a topological group G with multiplication defined pointwise.
See Loop (topology) and Loop group
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, i.e. continuous pointed maps from the pointed circle S1 to X, equipped with the compact-open topology. Loop (topology) and loop space are topology.
See Loop (topology) and Loop space
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Loop (topology) and Mathematics
Path (topology)
In mathematics, a path in a topological space X is a continuous function from a closed interval into X. Paths play an important role in the fields of topology and mathematical analysis. Loop (topology) and path (topology) are topology.
See Loop (topology) and Path (topology)
Pointed space
In mathematics, a pointed space or based space is a topological space with a distinguished point, the basepoint. Loop (topology) and pointed space are topology.
See Loop (topology) and Pointed space
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
See Loop (topology) and Princeton University Press
Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible.
See Loop (topology) and Quasigroup
Quotient space (topology)
In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the function that maps points to their equivalence classes). Loop (topology) and quotient space (topology) are topology.
See Loop (topology) and Quotient space (topology)
Topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.
See Loop (topology) and Topological space
Unit circle
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1.
See Loop (topology) and Unit circle
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. Loop (topology) and unit interval are topology.
See Loop (topology) and Unit interval
References
Also known as Loop (in topology).