Abstract
In this article we show that , the (Frechet) holomorphic functions on , is complete with respect to the topologies and . The same result for countable I is well known (see [2]) since in this case is a Frechet space. The extension to uncountable I requires a different approach.For the compact open topology we use induction to reduce the problem to the countable case.Next we use the result for to reduce the problem for and to the case of homogeneous polynomials.Using a method developed for holomorphic functions on nuclear Frechet spaces with a basis and, once more,the result for the compact open topology we complete the proof for and . We refer to [2] for background information.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
