Homeomorphic

In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. Very roughly speaking, a topological space is a geometric object, and a homeomorphism results from a continuous deformation of the object into a new shape. Thus, a square and a circle are homeomorphic to each other, but a sphere and a torus are not. However, this description can be misleading. Some continuous deformations do not result into homeomorphisms, such as the deformation of a line into a point. Some homeomorphisms do not result from continuous deformations, such as the homeomorphism between a trefoil knot and a circle. Homotopy and isotopy are precise definitions for the informal concept of continuous deformation.

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Tender - 2019-12-20T00:00:00.000000Z

Nightflyer - 2025-04-23T00:00:00.000000Z

Szelest - 2024-09-03T00:00:00.000000Z

Vulnerable - 2024-04-07T00:00:00.000000Z

Seeker - 2023-06-11T00:00:00.000000Z

Beautiful Mess - 2023-02-26T00:00:00.000000Z

The Well - 2023-02-05T00:00:00.000000Z

That Moment - 2022-11-18T00:00:00.000000Z

Hypnotizing - 2022-09-19T00:00:00.000000Z

Out of Reach - 2022-08-12T00:00:00.000000Z

Neons - 2022-06-10T00:00:00.000000Z

Drive ahead - 2022-04-28T00:00:00.000000Z

Long nights - 2022-04-20T00:00:00.000000Z

Dreamweaver - 2022-01-08T00:00:00.000000Z

Dissolation - 2021-12-31T00:00:00.000000Z

Eternal - 2021-12-28T00:00:00.000000Z

Revolutions - 2021-10-03T00:00:00.000000Z

Anthem - 2021-09-13T00:00:00.000000Z

Magnetic - 2021-05-21T00:00:00.000000Z

OXY - 2021-04-11T00:00:00.000000Z

Cienisty - 2021-03-09T00:00:00.000000Z

Luminar - 2020-12-12T00:00:00.000000Z

Dark Knight - 2020-11-05T00:00:00.000000Z

Aurose - 2020-10-25T00:00:00.000000Z

Submerged - 2020-07-31T00:00:00.000000Z