We study the behavior of limits of tangents in topologically equivalent spaces. In the context of families of generically reduced curves, we introduce the |$s$|-invariant of a curve and we show that in a Whitney equisingular family with the property that the |$s$|-invariant is constant along the parameter space, the number of tangents of each curve of the family is constant. In the context of families of isolated surface singularities, we show through examples that Whitney equisingularity is not sufficient to ensure that the tangent cones of the family are homeomorphic. We explain how the existence of exceptional tangents is preserved by Whitney equisingularity but their number can change.

中文翻译：

---

关于曲线和曲面的等价族的切线

我们研究拓扑等效空间中切线极限的行为。在一般减少的曲线族的背景下，我们引入| $ s $ | -曲线的不变量，我们证明在惠特尼等价族中，| $ s $ | -沿参数空间不变，该族的每条曲线的切线数不变。在孤立的表面奇异族的上下文中，我们通过示例证明惠特尼等奇性不足以确保该族的切线锥同胚。我们解释了惠特尼等奇性如何保留异常切线的存在，但是它们的数量可以改变。