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Equiuniform Quotient Spaces

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Abstract

The notion of a quotient space of a G-Tychonoff space is introduced. The universal property of this space is established.

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References

  1. P. Samuel, “On universal mappings and free topological groups,” Bull. Amer. Math. Soc. 54, 591–598 (1948).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Arhangel’skii and M. Tkachenko, Topological Groups and Related Structures (Atlantis Press, Paris, 2008).

    Book  MATH  Google Scholar 

  3. K. L. Kozlov, “Spectral decompositions of spaces induced by spectral decompositions of acting groups,” Topology Appl. 160 (11), 1188–1205 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  4. K. L. Kozlov and V. A. Chatyrko, “Topological transformation groups and Dugundji compacta,” Mat. Sb. 201 (1), 103–128 (2010) [Sb.Math. 201 (1), 103–128 (2010)].

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Engelking, General Topology (Heldermann Verlag, Berlin, 1989; “Mir,” Moscow, 1986).

    MATH  Google Scholar 

  6. J. R. Isbell, Uniform Spaces (Amer.Math. Soc., Providence, RI, 1964).

    Book  MATH  Google Scholar 

  7. M. G. Megrelishvili, “Compactification and factorization in the category of G-spaces,” in Categorical Topology and Its Relation to Analysis, Algebra and Combinatorics (World Sci., Singapore, 1989), pp. 220–237.

    Google Scholar 

  8. J. de Vries, “On the existence of G-compactifications,” Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (3), 275–280 (1978).

    MathSciNet  MATH  Google Scholar 

  9. M. G. Megrelishvili, “A Tichonov G-space not admitting a compact Hausdorff G-extension or G-linearization,” UspekhiMat. Nauk 43 (2 (260)), 145–146 (1988) [RussianMath. Surveys, 43 (2), 177–178 (1988)].

    MATH  Google Scholar 

  10. W. Kulpa, “Factorization and inverse expansion theorems for uniformities,” Colloq. Math. 21, 217–227 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  11. J. de Vries, Topological Transformation Groups 1. A Categorical Approach (Math. Centrum, Amsterdam, 1975).

    MATH  Google Scholar 

  12. S. MacLane, Categories for the Working Mathematician (Springer-Verlag, New York–Berlin, 1971; Fizmatlit, Moscow, 2004).

    MATH  Google Scholar 

  13. V. A. Chatyrko and K. L. Kozlov, “The maximal G-compactifications of G-spaces with special actions,” in Proceedings of the Ninth Prague Topological Symposium (Topol. Atlas, North Bay, ON, 2002), pp. 15–21.

    Google Scholar 

  14. K. L. Kozlov and V. A. Chatyrko, “On G-compactifications,” Mat. Zametki 78 (5), 695–709 (2005) [Math. Notes 78 (5), 649–661 (2005)].

    Article  MathSciNet  MATH  Google Scholar 

  15. K. L. Kozlov, “R-factorizable G-spaces,” Topology Appl. 227 (3), 146–164 (2017).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to E. V. Mart’yanov.

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Original Russian Text © E. V. Mart’yanov, 2018, published in Matematicheskie Zametki, 2018, Vol. 104, No. 6, pp. 872–894.

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Mart’yanov, E.V. Equiuniform Quotient Spaces. Math Notes 104, 866–885 (2018). https://doi.org/10.1134/S0001434618110317

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