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Continuity in the Coarse and Weak Shape Categories

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Abstract

The continuity theorems in the (abstract) coarse and weak shape categories are established. They also hold in the (standard) pointed and bi-pointed cases of topological spaces. An application of the bi-pointed continuity theorem in the standard (coarse) shape category is considered.

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References

  1. Engelking R.: General Topology. PWN - Polish Scientific Publishers, Warszawa (1977)

    MATH  Google Scholar 

  2. J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass.,1961.

  3. Keesling J., Mardešić S.: A shape fibration with fibers of different shape. Pacific J. Math 84, 319–331 (1979)

    MathSciNet  MATH  Google Scholar 

  4. Koceić Bilan N: On some coarse shape invariants. Topology Appl 157, 2679–2685 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Koceić Bilan N., Uglešić N.: The coarse shape, Glasnik. Mat 42(62), 145–187 (2007)

    MATH  Google Scholar 

  6. N. Koceić Bilan and N. Uglešić, The coarse shape path connectedness, Glasnik Mat. (in press).

  7. Mardešić S.: On covering dimension and inverse limits of compact spaces. Illinois J. Math 4, 278–291 (1960)

    MathSciNet  MATH  Google Scholar 

  8. Mardešić S: Products of compacta with polyhedra and topological spaces in the shape category, Mediterr. J. Math 1, 43–49 (2004)

    MATH  Google Scholar 

  9. S. Mardešić and J. Segal, Shape Theory, North-Holland, Amsterdam, 1982.

  10. Mardešić S., Uglešić N.: A category whose isomorphisms induce an equivalence relation coarser than shape, Top. Appl 153, 448–463 (2005)

    MATH  Google Scholar 

  11. Tholen W.: Pro-categories and multiadjoint functors, Can. J. Math 36, 144–155 (1984)

    MathSciNet  MATH  Google Scholar 

  12. Uglešić N.: Stability is a weak shape invariant. Glasnik Mat 44(64), 241–254 (2009)

    MATH  Google Scholar 

  13. Uglešić N., Červar B.: The concept of a weak shape type. International J. of Pure and Applied Math 39, 363–428 (2007)

    MATH  Google Scholar 

  14. Š. Ungar, A remark on shape paths and homotopy pro-groups, General Topology and its Relations to Modern Analysis and Algebra V, Proc. Fifth Prague Topology Symp., 1981, (J. Nowak, ed.), Heldermann-Verlag, Berlin, 1982, pp. 642–647.

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  1. University of Zadar, Pavlinovićeva bb, 23000, Zadar, Croatia

    Nikica Uglešić

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  1. Nikica Uglešić
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Correspondence to Nikica Uglešić.

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Uglešić, N. Continuity in the Coarse and Weak Shape Categories. Mediterr. J. Math. 9, 741–766 (2012). https://doi.org/10.1007/s00009-011-0148-2

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  • DOI: https://doi.org/10.1007/s00009-011-0148-2

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