A relation $R$ is serial iff $\forall x, \exists y, xRy$. What is the name of the inverse property stating that $\forall y, \exists x, xRy$? And is there a name for the property which is the conjunction of both previous ones?
2026-04-09 02:04:04.1775700244
What is the term for a relation whose inverse relation is serial?
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According to Proof wiki, the first thing you are asking about ($\forall y\exists x(xRy)$) can be called a right total relation, and the thing you defined as "serial relation" may be called a left total relation.
They mention that a right-and-left total relation may be called a total relation on the left total relation page, but caution you not to confuse it with a "connected relation."