The notion of parametrized topological complexity, introduced by Cohen, Farber and Weinberger, is extended to fiberwise spaces which are not necessarily Hurewicz fibrations. After exploring some formal properties of this extension we also introduce the pointed version of parametrized topological complexity. Finally, we give sufficient conditions so that both notions agree.

中文翻译：

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参数化拓扑复杂性的形式方面及其尖锐版本

由 Cohen、Farber 和 Weinberger 提出的参数化拓扑复杂性的概念被扩展到不一定是 Hurewicz 纤维的纤维空间。在探索了该扩展的一些形式属性之后，我们还介绍了参数化拓扑复杂性的尖峰版本。最后，我们给出充分的条件以使两个概念一致。