On Higher Effective Descriptive Set Theory

In the framework of computable topology, we propose an approach how to develop higher effective descriptive set theory. We introduce a wide class \(\mathbb {K}\) of effective \(T_0\)-spaces admitting Borel point recovering. For this class we propose the notion of an \((\alpha ,m)\)-retractive morphism that gives a great opportunity to extend classical results from EDST to the class \(\mathbb {K}\). We illustrate this by several examples.

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