Phrase guide

complex projective line

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 1

A complex line (especially, the set of complex numbers regarded as such) endowed with a point at infinity (thus becoming a projective line); (more formally) the set of equivalence classes of ordered pairs (α, β) of complex numbers, not both zero, with respect to the equivalence relation "(α, β) ≡ (λα, λβ) for all nonzero complex λ".

Definition source: English Wiktionary via Wiktextract

Usage: analytic

Qualifier: projective geometry

Topics: geometry, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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Across languages

Translations

1 source translations are retained for this English entry.

  • Polish: sfera Riemanna — complex numbers plus point at infinity — see also Riemann sphere