On Higher Effective Descriptive Set Theory

摘要

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