This essay advances a structural account of identity through change by reframing space as the condition of transition rather than a passive container. It argues that every transition between states contains a continuous infinite interior—an asymptotically traversed distance that admits no boundary. Because replacement requires a boundary at which one state ceases and another begins, a continuous interior precludes replacement and preserves identity as continuous modification rather than succession. On this basis, the persistence of the self is not grounded in memory, material continuity, or narrative coherence, but in the topology of transition itself. The human self is understood as an irreducible unit that remains numerically identical through change by continuously traversing this interior at the point of actualization, the Now. The argument is developed through engagement with classical and modern accounts of identity and becoming, and concludes by examining the necessity of a sustaining ground that holds both temporal actualization and continuous transition open. Identity is thus preserved not despite change, but through it, as a consequence of the absence of ontological boundaries within transition.
Oscar Gaitan (Mon,) studied this question.