homeomorphism

1 9.9

A change of one shape into another by stretching and bending that can be reversed without cutting or gluing

noun
/ˌhoʊmiˈɔrfɪzəm/

Specialized

: homeomorfismo

In topology, a homeomorphism is essential for proving that two spaces are topologically equivalent.

Examples

The sets U on the manifold are the regions of the globe which are represented by the corresponding charts U', and the homeomorphisms ensure that the representations are one-to-one and onto.

Academic text (1998)
Since, because of the homeomorphism, this perception is like a local portion of Euclidean space, this phenomenon is well-founded. This means that the Euclidean structure is not an exterior import of the reflections of a higher monad; it is a locally obtaining structure of the perceptual-monadic world.

Academic text (1998)
The homeomorphism is not sufficient to completely secure the well-foundedness of phenomena.

Academic text (1998)
A homeomorphism allows us to understand how two different shapes can be transformed into one another without cutting or gluing.
The mathematician demonstrated a homeomorphism between the circle and an ellipse, illustrating their topological similarity.

Surface Forms

homeomorphism singular

homeomorphisms plural

Morphology

homeomorphism = morphism (opaque) = homeo + morphism

A technical mathematical coinage combining Greek-derived combining forms; average learners will not derive the precise technical meaning from the parts.

Etymology

Homeomorphism comes from the parts homeo- meaning 'same' and -morphism meaning 'form' or 'shape', like the English word 'form'. So a homeomorphism is a 'same-form' map that shows two objects can be stretched or bent into each other without tearing.