Skip to main content
SpringerLink
Log in

Approach Theory in Merotopic, Cauchy and Convergence Spaces. I

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We introduce the notions of approach-merotopic structure and approach-filter merotopic structure by means of a map assigning to a collection of sets 'smallness' of members and define categories AMER and AFIL containing MER and FIL as bireflectively and bicoreflectively embedded subcategories, respectively. We show that the category AMER is a topological construct and AFIL which is a supercategory of ps-MET ∞ as well is a cartesian closed topological category bicoreflectively embedded in AMER.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. L. Bentley, H. Herrlich and E. Lowen-Colebunders, The category of Cauchy spaces is cartesian closed, Topology and its Applications, 27 (1987), 105–112.

    Google Scholar 

  2. H. L. Bentley, H. Herrlich and E. Lowen-Colebunders, Convergence, Journal of Pure and Applied Algebra, 68 (1990), 27–45.

    Google Scholar 

  3. H. Herrlich, Topological structures, Mathematical Centre Tracts, 52 (1974), 125–142.

    Google Scholar 

  4. H. Herrlich and G. Strecker, Category Theory, Allyn and Bacon (1973).

  5. M. Katětov, On continuity structures and spaces of mappings, Comm. Math. Univ. Car., 6 (1965), 257–278.

    Google Scholar 

  6. E. Lowen-Colebunders, Function Classes of Cauchy Continuous Maps, Pure and applied mathematics 123, Marcel Dekker, Inc. (New York, 1989).

    Google Scholar 

  7. E. Lowen and R. Lowen, A quasitopos containing CONV and MET as full subcategories, Internat. J. Math. & Math. Sci., 11 (1988), 417–438.

    Google Scholar 

  8. R. Lowen, Approach Spaces: The Missing Link in the Topology-Uniformity-Metric-Triad, Oxford Mathematical Monographs, Oxford University Press (1997).

  9. R. Lowen and K. Robeys, Completions of products of metric spaces, Quart. J. Math. Oxford, 43 (1992), 319–338.

    Google Scholar 

  10. R. Lowen and K. Robeys, Compactifications of products of metric spaces and their relations to Čech-Stone and Smirnov compactifications, Topology and its Applications, 55 (1994), 163–183.

    Google Scholar 

  11. R. Lowen and D. Vaughan, A completion for T 0 approach spaces, submitted for publication.

  12. G. Preuss, Theory of Topological Structures, D. Reidel Publishing Company (1988).

  13. W. Robertson, Convergence as a nearness concept, Thesis Carleton University Ottawa (Ontario, 1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. R.U.C.A. Department of Mathematics and Computer Science, University of Antwerp, Groenenborgerlaan 171, 2020, Antwerp, Belgium

    R. Lowen

  2. Department of Mathematics, Yonsei University, Seoul, Korea, 120-749

    Yoon Jin Lee

Authors
  1. R. Lowen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yoon Jin Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lowen, R., Lee, Y.J. Approach Theory in Merotopic, Cauchy and Convergence Spaces. I. Acta Mathematica Hungarica 83, 189–207 (1999). https://doi.org/10.1023/A:1006717022079

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006717022079

Keywords

Search

Navigation