论文信息 - Computability and Representations of the Zero Set

Computability and Representations of the Zero Set

In this note we give a new representation for closed sets under which the robust zero set of a function is computable. We call this representation the component cover representation. The computation of the zero set is based on topological index theory, the most powerful tool for finding robust solutions of equations.

Pieter Collins

[1] 坂上貴之. 書評 Computational Homology , 2005 .

[2] RobertF Brown,et al. The Lefschetz fixed point theorem , 1971 .

[3] James R. Munkres,et al. Elements of algebraic topology , 1984 .

[4] Klaus Weihrauch,et al. Computable Analysis: An Introduction , 2014, Texts in Theoretical Computer Science. An EATCS Series.

[5] Klaus Weihrauch,et al. Computable Analysis , 2005, CiE.

[6] Vasco Brattka. Effective Borel measurability and reducibility of functions , 2005, Math. Log. Q..

[7] R. Ho. Algebraic Topology , 2022 .

[8] J. Craggs. Applied Mathematical Sciences , 1973 .

[9] J. Milnor. Topology from the differentiable viewpoint , 1965 .

[10] Paul Taylor,et al. A lambda calculus for real analysis , 2010, J. Log. Anal..