The present paper investigates a strong homotopy (i.e., SA-homotopy) in a finite topological adjacency category. We prove that two minimal finite spaces are SA-homotopy equivalent if and only if they are A-isomorphic in the category, and that two finite $T_0$-spaces are SA-homotopy equivalent if and only if they have A-isomorphic cores. As an application, we prove that all simple closed KA-curves are not SA-contractible. The SA-homotopy is a generalization of the classical topological homotopy. We also reveal similar properties between SA-homotopy and the classical topological homotopy. Moreover, in the sense of SA-homotopy we answer two questions having close relationships with that posed by Boxer (2005) [4].

本论文研究了有限拓扑邻接范畴中的强同伦（即SA同伦）。我们证明两个极小有限空间是SA 同伦等价的当且仅当它们在范畴中是A 同构的，并且两个有限空间${吨}_0$-spaces 是SA -同伦等价的当且仅当它们具有A -同构核。作为一个应用，我们证明所有简单的封闭KA曲线都不是SA 可收缩的。该SA -homotopy是经典拓扑同伦的推广。我们还揭示了SA同伦和经典拓扑同伦之间的相似性质。此外，在SA 同伦的意义上，我们回答了与 Boxer (2005) [4] 提出的问题密切相关的两个问题。