Twisted Products: Enveloping Actions and Equivariant Absolute Neighborhood Extensors

The classical concept of a twisted product is examined within the framework of partial actions. Specifically, we demonstrate that the globalization of a partial action results in a twisted product. Additionally, we outline conditions for the metrizability of twisted products and prove certain homotopy and categorical properties. Moreover, sufficient conditions are established for the enveloping space to be an equivariant absolute neighborhood extensor.