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Functional equivalence of topological spaces and topological modules

Year 2017, Volume: 46 Issue: 1, 77 - 90, 01.02.2017

Abstract

Let $R$ be a topological ring and $E$, $F$ be unitary topological $R$-modules. Denote by $C_p(X,E)$ the class of all continuous mappings of $X$ into $E$ in the topology of pointwise convergence. The spaces $X$ and $Y$ are called $l_p(E,F)$-equivalent if the topological $R$-modules $C_p(X,E)$ and $C_p(Y,F)$ are topological isomorphic. Some conditions under which the topological property $\mathcal{P}$ is preserved by the $l_p(E,F)$-equivalence (Theorems 6.3, 6.4, 7.3 and 8.1) are given.

References

  • A. V. Arhangel'skii, Topological Function Spaces, Mathematics and its Applications (Soviet Series), vol. 78, Kluwer Academic Publishers Group, Dordrecht, 1992.
  • A. V. Arhangel'skii, On linear homomorphisms of function spaces, Doklady Acad. Nauk SSSR 264 (1982), no. 6, 1289-1292. English translation: Soviet Math. Dokl. 25 (1982), 852-855.
  • M.M. Choban, General theorems on functional equivalence of topological spaces, Topology Appl. 89 (1998), 223-239.
  • M.M. Choban, Algebraical equivalence of topological spaces, Buletinul Acad. de “tiinµe a Republicii Moldova, Matematica, 1 (2001), 12-36.
  • M. Choban, Open finite-to-one mappings, Soviet Math. Dokl. 8 (1967), 603-603.
  • M.M. Choban, On the theory of topological algebraic systems, Trudy Moskovskogo Matem. Obshchestva 48 (1985), 106-149. English translation: Trans. Moscow Math. Soc. 48, 1986, 115-159.
  • M.M. Choban, Some topics in topological algebra, Topology Appl. 54 (1993), 183-202.
  • M.M. Choban, R. N. Dumbraveanu, $l_p(R)$-equivalence of topological spaces and topological modules, Buletinul Academiei de Stiinte a Rep. Moldova, Matematica 1 (2015), 20-47.
  • R. Engelking, General Topology, PWN, Warsawa 1977.
  • J. S. Golan, Semirings and their applications, Springer, 1999.
  • V. P. Maslov, Idempotent analysis, American Mathematical Society, 1992.
  • J. van Mill, The infinite-dimensional topology of function spaces, North-Holland Mathemat- ical Library, Amsterdam, vol. 64, 2001.
  • A. Okuyama, A survey of the theory of $\sigma$-spaces, General Topology Appl. 1 (1971), 57-63.
  • V. Valov, Function spaces, Topology Appl. 81 (1997), no. 1, 1-22.
  • S. Warner, Topological rings, North-Holland mathematics studies. Elsevier, v. 178, 1993.
Year 2017, Volume: 46 Issue: 1, 77 - 90, 01.02.2017

Abstract

References

  • A. V. Arhangel'skii, Topological Function Spaces, Mathematics and its Applications (Soviet Series), vol. 78, Kluwer Academic Publishers Group, Dordrecht, 1992.
  • A. V. Arhangel'skii, On linear homomorphisms of function spaces, Doklady Acad. Nauk SSSR 264 (1982), no. 6, 1289-1292. English translation: Soviet Math. Dokl. 25 (1982), 852-855.
  • M.M. Choban, General theorems on functional equivalence of topological spaces, Topology Appl. 89 (1998), 223-239.
  • M.M. Choban, Algebraical equivalence of topological spaces, Buletinul Acad. de “tiinµe a Republicii Moldova, Matematica, 1 (2001), 12-36.
  • M. Choban, Open finite-to-one mappings, Soviet Math. Dokl. 8 (1967), 603-603.
  • M.M. Choban, On the theory of topological algebraic systems, Trudy Moskovskogo Matem. Obshchestva 48 (1985), 106-149. English translation: Trans. Moscow Math. Soc. 48, 1986, 115-159.
  • M.M. Choban, Some topics in topological algebra, Topology Appl. 54 (1993), 183-202.
  • M.M. Choban, R. N. Dumbraveanu, $l_p(R)$-equivalence of topological spaces and topological modules, Buletinul Academiei de Stiinte a Rep. Moldova, Matematica 1 (2015), 20-47.
  • R. Engelking, General Topology, PWN, Warsawa 1977.
  • J. S. Golan, Semirings and their applications, Springer, 1999.
  • V. P. Maslov, Idempotent analysis, American Mathematical Society, 1992.
  • J. van Mill, The infinite-dimensional topology of function spaces, North-Holland Mathemat- ical Library, Amsterdam, vol. 64, 2001.
  • A. Okuyama, A survey of the theory of $\sigma$-spaces, General Topology Appl. 1 (1971), 57-63.
  • V. Valov, Function spaces, Topology Appl. 81 (1997), no. 1, 1-22.
  • S. Warner, Topological rings, North-Holland mathematics studies. Elsevier, v. 178, 1993.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Mitrofan M. Choban

Radu N. Dumbraveanu This is me

Publication Date February 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 1

Cite

APA Choban, M. M., & Dumbraveanu, R. N. (2017). Functional equivalence of topological spaces and topological modules. Hacettepe Journal of Mathematics and Statistics, 46(1), 77-90.
AMA Choban MM, Dumbraveanu RN. Functional equivalence of topological spaces and topological modules. Hacettepe Journal of Mathematics and Statistics. February 2017;46(1):77-90.
Chicago Choban, Mitrofan M., and Radu N. Dumbraveanu. “Functional Equivalence of Topological Spaces and Topological Modules”. Hacettepe Journal of Mathematics and Statistics 46, no. 1 (February 2017): 77-90.
EndNote Choban MM, Dumbraveanu RN (February 1, 2017) Functional equivalence of topological spaces and topological modules. Hacettepe Journal of Mathematics and Statistics 46 1 77–90.
IEEE M. M. Choban and R. N. Dumbraveanu, “Functional equivalence of topological spaces and topological modules”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 1, pp. 77–90, 2017.
ISNAD Choban, Mitrofan M. - Dumbraveanu, Radu N. “Functional Equivalence of Topological Spaces and Topological Modules”. Hacettepe Journal of Mathematics and Statistics 46/1 (February 2017), 77-90.
JAMA Choban MM, Dumbraveanu RN. Functional equivalence of topological spaces and topological modules. Hacettepe Journal of Mathematics and Statistics. 2017;46:77–90.
MLA Choban, Mitrofan M. and Radu N. Dumbraveanu. “Functional Equivalence of Topological Spaces and Topological Modules”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 1, 2017, pp. 77-90.
Vancouver Choban MM, Dumbraveanu RN. Functional equivalence of topological spaces and topological modules. Hacettepe Journal of Mathematics and Statistics. 2017;46(1):77-90.