In this paper, we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space. As a corollary, we generalize results in [Artigue et al. Beyond topological hyperbolicity: the Lshadowing property, J. Differ. Equ. 268(6) (2020), pp. 3057–3080.] and [Carvalho and Cordeiro, Positively N-expansive homeomorphisms and the L-shadowing property, J. Dyn. Differ. Equ. 31(2) (2019), pp. 1005–1016.] proving that positively countably expansive homeomorphisms defined on compact metric spaces satisfying either transitivity and the shadowing property, or the L-shadowing property, can only be defined in countable spaces.

在本文中，我们研究具有紧度量空间上定义的阴影属性的敏感同胚的局部稳定/不稳定集。我们证明局部稳定/不稳定集总是包含空间的紧凑且完美的子集。作为推论，我们概括了 [Artigue 等人。超越拓扑双曲性：Lshadowing 性质，J. Differ。等式。268(6) (2020)，第 3057–3080 页。] 和 [Carvalho 和 Cordeiro，正 N 扩张同胚和 L 遮蔽性质，J. Dyn。不同。等式。31(2) (2019), pp. 1005–1016.]证明在满足传递性和阴影性质或L-阴影性质的紧度量空间上定义的正可数扩张同胚只能在可数空间中定义。