Remarks on smooth real-compactness for Sikorski spaces

• Autorzy: Cukrowski, M. J. , Stronkowski, M. M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

PL

przestrzeń Sikorskiego

EN

Sikorski spaces; smooth real-compactness

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 2
• Strony: 465--473
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Cukrowski, M. J.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland,

autor

Stronkowski, M. M.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland,

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