Abstract
Suppose that an ideal $J$ of $C^\infty$ functions on an open subset of $\mathbf{R}^2$ is a Łojasiewicz ideal. We describe the set of $C^\infty$ functions vanishing on the zeros of $J$ explicitly using $J$ in an open neighborhood of each point in zeros of $J$, it can be obtained by taking real radical and closure starting from $J$ repeatedly for a finite number of times. This gives an another affirmative answer to Bochnak's conjecture in dimension 2, which is first done by Risler.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.