Number & MeasureGreek → English
Homeomorphism
/ˌhoʊmiəˈmɔːrfɪzəm/noun
A continuous one-to-one map between topological spaces whose inverse is also continuous, making the two spaces the same for topological purposes.
The Greek roots
ὅμοιος
hómoios
similar, of like kind
μορφή
morphḗ
form, shape
Literally: “similar-shapedness”
The story of the word
The single letter separating homeomorphism from homomorphism is a real Greek distinction: ὅμοιος means similar, ὁμός means identical. Mathematicians borrowed both and gave them different jobs, one in topology and one in algebra, so mispronouncing the word changes the subject. Poincaré was using homéomorphisme in the 1890s while working out analysis situs, the field now called topology.
- How it travelled
- Ancient Greek → scientific coinage → English
- First recorded
- 20th century
Same family
homoeopathymorphologyamorphousmetamorphosis
In a sentence
The old joke about the doughnut and the coffee cup is a statement that the two are homeomorphic.