Skip to main content
SpringerLink
Log in

Filter spaces

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

The category FIL of filter spaces and cauchy maps is a topological universe. This paper establishes the foundation for a completion theory forT 2 filter spaces.

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: Convergence,J. Pure Appl. Algebra 68 (1990), 27–45.

    Google Scholar 

  2. H.L. Bentley, H. Herrlich, and W.A. Robertson: Convenient categories for topologists,Comment. Math. Univ. Carolinae 17 (1976), 207–227.

    Google Scholar 

  3. C.H. Cook and H.R. Fischer: Uniform convergence structures,Math. Ann. 137 (1959), 269–303.

    Google Scholar 

  4. H.H. Keller: Die Limes-Uniformisierbarkeit der Limesraume,Math. Ann. 176 (1968), 334–341.

    Google Scholar 

  5. M. Katetov: Allgemeine Stetigkeitsstrukturen,Proc. Intern. Congr. Math. Stockholm 1962 (1963), 473–479.

    Google Scholar 

  6. M. Katetov: On continuity structures and spaces of mappings,Comment. Math. Univ. Carolinae 6 (1965), 257–278.

    Google Scholar 

  7. D.C. Kent and G.D. Richardson: Regular completions of Cauchy spaces,Pacific J. Math. 51 (1974), 483–490.

    Google Scholar 

  8. D.C. Kent and G.D. Richardson: Cauchy spaces with regular completions,Pacific J. Math. 111 (1984), 105–116.

    Google Scholar 

  9. D.C. Kent and G.D. Richardson: Cauchy completion categories,Canad. Math. Bull. 32 (1989), 78–84.

    Google Scholar 

  10. G. Preuss:Theory of Topological Structures, D. Reidel Publ. Co., Dordrecht, 1988.

    Google Scholar 

  11. G. Preuss: Improvement of Cauchy spaces,Q&A in General Topology 9 (1991), 159–166.

    Google Scholar 

  12. E.E. Reed: Completions of uniform convergence spaces,Math. Ann. 194 (1971), 83–108.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Pure and Applied Mathematics, Washington State University, 99163, Pullman, WA, USA

    D. C. Kent & Nandita Rath

Authors
  1. D. C. Kent
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nandita Rath
    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

Kent, D.C., Rath, N. Filter spaces. Appl Categor Struct 1, 297–309 (1993). https://doi.org/10.1007/BF00873992

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00873992

Mathematics Subject Classifications (1991)

Key words

Search

Navigation