Remarks on Smooth Real-Compactness for Sikorski Spaces

Abstract: It is known that every Sikorski space with the countably generated differential structure is smoothly real-compact. It means that every homomorphism from its differential structure, which forms a ring of smooth real-valued functions into the ring of real numbers, is an evaluation. This result is sharp: there is a non-smoothly real-compact Sikorski space with the differential structure which is not countably generated. We provide an easy example demonstrating this. By modifying this example we are able to show a certain shortcoming of the generator embedding, comparing to the canonical embedding, for Sikorski spaces. Finally, we note that a homomorphism from the ring of smooth functions of a Sikorski space into the ring of real numbers is an evaluation if and only if it is continuous.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Remarks on Smooth Real-Compactness for Sikorski Spaces ; volume:47 ; number:2 ; year:2014 ; pages:465-473 ; extent:9 ; Demonstratio mathematica ; 47, Heft 2 (2014), 465-473 (gesamt 9)

Contributors, Places and Time

• Creator: Cukrowski, Michał J. ; Stronkowski, Michał M.

Further information

• DOI: 10.2478/dema-2014-0037
• URN: urn:nbn:de:101:1-2411181534051.580090161419
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:37 AM CEST