Skip to main content
SpringerLink
Log in

Convergence Approach Spaces : Actions

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

Properties of continuous actions and pseudoquotients are studied in the category of convergence approach spaces. Invariance properties of continuous actions on convergence approach spaces are given. It is shown that the formation of pseudoquotient spaces is idempotent. Function space actions are also investigated.

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. Boustique, H., Mikusiński, P., Richardson, G.: Convergence semigroup categories. Appl. Gen. Top. 11, 67–88 (2010)

    MathSciNet  MATH  Google Scholar 

  2. Brock, P., Kent, D.: Approach spaces, limit tower spaces, and probabilistic convergence spaces. Appl. Categ. Struct. 5, 99–110 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Burzyk, J., Ferens, C., Mikusiński, P.: On the topology of generalized quotients. Appl. Gen. Top 9, 205–212 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Colebunders, E., Mynard, F., Trott, W.: Function spaces and contractive extensions in approach theory : the role of regularity. Appl. Categ. Struct. 22, 551–563 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. De Graaf, J., Elst, A.F.M.: An algebraic approach to distribution theories Proceedings of the international conference on Generalized Functions, Convergence Structures, and Their Applications, Dubrovnik (1987), pp 171–177. Plenum Press, New York (1988)

    Chapter  Google Scholar 

  6. Katsevich, A., Mikusiński, P.: On De Graaf spaces of pseudoquotients, Rocky Mtn. J. Math. (to appear)

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Lowen, R.: Approach spaces: the missing link in topology-uniformity-metric triad. OxfordMathematical Monographs, Oxford University Press (1997)

  9. Lowen, R., Windels, B.: Approach groups. Rocky Mtn. J. Math 30, 1057–1073 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mikusiński, P.: Boehmians and generalized functions. Acta. Math. Hungar. 51, 271–281 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mikusiński, P.: Generalized quotients with applications in analysis. Methods Appl. Anal 10, 377–386 (2003)

    MathSciNet  MATH  Google Scholar 

  12. Mikusiński, P., Purtee, S.: Connectedness in spaces of pseudoquotients. Topol. Proc. 40, 283–288 (2012)

    MathSciNet  MATH  Google Scholar 

  13. Park, W.: Convergence structures on homeomorphism groups. Math. Ann 199, 45–54 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  14. Rath, N.: Action of convergence groups. Topol. Proc. 27, 601–612 (2003)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vakgroep Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussel, Belgie

    E. Colebunders

  2. Department of Mathematics, Valencia College, 701 N. Econlockhatchee Trail, Orlando, 32825, Florida

    H. Boustique

  3. Department of Mathematics, University of Central Florida, 4393 Andromeda Loop N, Orlando, 32816, Florida

    P. Mikusiński & G. Richardson

Authors
  1. E. Colebunders
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Boustique
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Mikusiński
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. Richardson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Boustique.

Additional information

Dedicated to Professor D.C. Kent on his 81th birthday

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Colebunders, E., Boustique, H., Mikusiński, P. et al. Convergence Approach Spaces : Actions. Appl Categor Struct 24, 147–161 (2016). https://doi.org/10.1007/s10485-015-9390-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10485-015-9390-2

Keywords

Mathematics Subject Classification (2010)

Search

Navigation