Abstract
The present note deals with the same subject as the investigations by M. Stone (2) and the note of G. Šilov published above. In difference from this last note, we consider a ring of continuous functions defined on a rertain topological space as a purely algebraical formation, without introducing in it any topological relations. It turns out that in the case of bicompact spaces considered by M. Stone, as well as in considerably more general cases, the algebraical structure of the ring of continuous functions already defines the topological space up to a homeomorphism.
(Communicated by I. M. Vinogradov, Member of the Academy, 17. XI. 1938)
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References
E. Čech, Annais of Mathematics, 38, 823–844 (1937).
M. H. Stone, Trans. American Math. Soc., 41, 375–481 (1937).
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© 1993 Miroslav Katětov, Petr Simon et al.
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Gelfand, I., Kolmogoroff, A. (1993). On Rings of Continuous Functions on Topological Spaces. In: Katětov, M., Simon, P. (eds) The Mathematical Legacy of Eduard Čech. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7524-0_5
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