Loop (topology)

In today's world, Loop (topology) has become a topic of growing interest and debate in different areas. From politics to science, through culture and society, Loop (topology) has managed to capture the attention of a large number of people around the world. Its implications, its impact and its relevance have generated a wide range of opinions, theories and studies that seek to understand and analyze this phenomenon in depth. In this article, we will explore different aspects related to Loop (topology), from its origins to its influence today, with the aim of providing a complete and updated vision of this topic that is so relevant today.

Topological path whose initial point is equal to its terminal point

In mathematics, a loop in a topological space X is a continuous function f from the unit interval I = to X such that f(0) = f(1). In other words, it is a path whose initial point is equal to its terminal point.^[1]

A loop may also be seen as a continuous map f from the pointed unit circle S¹ into X, because S¹ may be regarded as a quotient of I under the identification of 0 with 1.

The set of all loops in X forms a space called the loop space of X.^[1]

See also

• Free loop
• Loop group
• Loop space
• Loop algebra
• Fundamental group
• Quasigroup

References

1. ^ ^{a b} Adams, John Frank (1978), Infinite Loop Spaces, Annals of mathematics studies, vol. 90, Princeton University Press, p. 3, ISBN 9780691082066.

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