Skip to main content
SpringerLink
Log in

Foundational Isomorphisms in Continuous Differentiation Theory

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

We provide an elementary proof of existence for the Foundational Isomorphism in each of the categories of convergence spaces, compactly generated topological spaces and sequential convergence spaces. This isomorphism embodies the ‘germ’ of differentiation and its inverse the ‘germ’ of integration.

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. Binz, E.: Continuous convergence on C(X), Lecture Notes in Math. 469, Springer-Verlag, Berlin, 1975.

    Google Scholar 

  2. Nel, L. D.: Infinite dimensional calculus allowing nonconvex domains with empty interior, Monatsh. Math. 110(1990), 145-166.

    Google Scholar 

  3. Nel, L. D.: Introduction to Categorical Methods(Parts One and Two), Carleton-Ottawa Mathematical Lecture Note Series 11, Carleton University, 1991.

  4. Nel, L. D.: Introduction to Categorical Methods(Part Three), Carleton-Ottawa Mathematical Lecture Note Series 12, Carleton University, 1991.

  5. Nel, L. D.: Effective categories of complete separated spaces, Recent Developments of General Topology and its Applications(International conference in memory of Felix Hausdorff, Berlin, 1992), Akademie Verlag, Berlin, 1992, 242-251.

    Google Scholar 

  6. Nel, L. D.: Differential calculus founded on an isomorphism, Appl. Categorical Structures 1(1993), 51-57.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Churgbuk National University, Cheongju, 360-763, South Korea

    S. J. Lee

  2. Department of Mathematics and Statistics, Carleton University, Ottawa, Ont., Canada, K1S 5B6

    L. D. Nel

Authors
  1. S. J. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. D. Nel
    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

Lee, S.J., Nel, L.D. Foundational Isomorphisms in Continuous Differentiation Theory. Applied Categorical Structures 6, 127–135 (1998). https://doi.org/10.1023/A:1008631405316

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008631405316

Search

Navigation