also: かいせい
noun which may take the genitive case particle 'no', noun
matchless; peerless; overwhelming; world-dominating
Formal or literary term used to describe exceptional heroism, spirit, resolve, or power that surpasses all others. Often appears in set phrases like 蓋世の英雄 (a hero without equal) or 蓋世の気概 (unrivaled spirit).
彼は蓋世の英雄として歴史に名を残した。
He left his name in history as a peerless hero.
その
The athlete faced the match with overwhelming fighting spirit.
無双 also means 'peerless' or 'unmatched', but is more common in modern Japanese and often used in gaming or competitive contexts. 蓋世 is more literary and emphasizes world-surpassing greatness.
天下無敵 means 'invincible under heaven' and is more colloquial. 蓋世 carries a more formal, classical nuance of dominating an era or the world.
From Chinese 蓋世 (gàishì), literally 'covering the world', meaning to surpass or dominate one's era. The exact historical derivation is uncertain, but the spelling is conventionally associated with this meaning.