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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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About the density property in the space of continuous maps vanishing at infinity; pp. 282–290

(Full article in PDF format) https://doi.org/10.3176/proc.2018.3.07


Authors

Mart Abel

Abstract

The conditions when C0(X)⊗Y is dense in C0(X;Y) in the compact-open topology on C0(X;Y) are given. This result is used for describing the properties of topological Segal algebras.

Keywords

Segal algebra, density property, approximation property, algebra of continuous functions vanishing at infinity.

References

1. Abel , Mart. Generalisation of Segal algebras for arbitrary topological algebras. Period. Math. Hung.https://link.springer.com/article/10.1007/s10998-017-0222-z (accessed 2018–05–11).

2. Abel , Mati. The denseness everywhere of subsets in some spaces of vector-valued functions (in Russian). Tartu Riikl. Ül. Toimetised , 1987 , 770 , 26–37.

3. Aleksandrov , P. S. and Pasynkov , B. A. Introduction to Dimension Theory (in Russian). Nauka , Moscow , 1973.

4. Gillman , L. and Jerison , M. Rings of Continuous Functions. The University Series in Higher Mathematics. D. Van Nostrand Co. , Inc. , Princeton , N.J.–Toronto–London–New York , 1960.
https://doi.org/10.1007/978-1-4615-7819-2

5. Górniewicz , L. and Ślosarski , M. Fixed points of mappings in Klee admissible spaces. Control Cybernet. , 2007 , 36(3) , 825–832.

6. Horváth , J. Topological Vector Spaces and Distributions. Vol. I. Addison-Wesley Publishing Co. , Reading , Mass.–London–Don Mills , Ont. , 1966.

7. Husain , T. Introduction to Topological Groups. R. E. Krieger Publ. Co. , Philadelphia , 1981.

8. Kantorovich , L. V. and Akilov , G. P. Functional Analysis. (Translated form the Russian by Howard L. Silcock). Second Edition. Pergamon Press , Oxford–Elmsford , N. Y. , 1982.

9. Rudin , W. Real and Complex Analysis. McGraw-Hill Book Co. , New York–Toronto , Ont.–London , 1966.

10. Shuchat , A. H. Approximation of vector-valued continuous functions. Proc. Am. Math. Soc. , 1972 , 31(1) , 97–103.
https://doi.org/10.1090/S0002-9939-1972-0290082-5

11. Thomsen , K. More on locally compact Haudorff spaces , http://data.math.au.dk/kurser/advanalyse/F06/lecture11pr.pdf (2005) (accessed 2017–02–03).

12. Waelbroeck , L. Topological vector spaces. In Summer School on Topological Vector Spaces. Held at the Universit´e Libre de Bruxelles , Brussels , in September 1972 (Waelbroeck , L. , ed.). Lecture Notes in Math. , 331. Springer-Verlag , Berlin–New York , 1977 , 1–40.

 
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Current Issue: Vol. 69, Issue 2, 2020




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December