Etymology
The word "homeomorphism" is derived from the Greek words:
Meaning
In mathematics, a homeomorphism is a bijective continuous function between two topological spaces that preserves the topological structure of both spaces. In other words, it is a function that stretches, bends, and distorts the first space into the second space without tearing or gluing anything together.
Origin
The concept of homeomorphism first emerged in the late 19th century in the work of French mathematician Henri Poincaré. Poincaré originally referred to such mappings as "continuous one-to-one correspondences" or "continuous bijections."
The term "homeomorphism" was first introduced in 1911 by German mathematician Georg Cantor. Cantor used the term to describe a particular type of mapping between transfinite sets, but it was later adopted by topologists to refer more generally to continuous bijections between topological spaces.
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