fundamental group
Word Rarity
Uncommon
Frequency: Zipf frequency 4.31 in modern English
25
Scrabble Score
16
Letters
5
Syllables
13
Unique Chars
Meaning
noun
For a specified topological space, the group whose elements are homotopy classes of loops (images of some arbitrary closed interval whose endpoints are both mapped to a designated point) and whose group operation is concatenation.
Example Sentences
- "From the definition it will be clear the group is a topological invariant of X; i.e., if two spaces are homeomorphic, their fundamental groups are isomorphic."
- "Therein came into focus the far-reaching vision that the perspective of non-abelian fundamental groups could lead to a fundamentally new understanding of deep arithmetic phenomena, including the arithmetic theory of moduli and Diophantine finiteness on hyperbolic curves."
- "During the more than 100 years of its existence, the notion of the fundamental group has undergone a considerable evolution."
Inflected Forms
Phrases
Frequently Paired Words
fundamental groupoid