Skip to main content
SpringerLink
Log in

Compatibility of book-spaces with certain identities

  • Published:
Algebra universalis Aims and scope Submit manuscript

Abstract

This paper is a brief study of the equations compatible with the (topological) n-book for all \({n \geq 2}\). For each n, we exhibit an equation-set (an extension of lattice theory) that is identically satisfiable on the \({(n + 1)}\)-book, but not on the n-book.

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. Alexandroff P.: Diskrete Räume. Mat. Sb., N.S. 2 44, 501–519 (1937)

    MATH  Google Scholar 

  2. Anderson L.W.: On the distributivity and simple connectivity of plane topological lattices. Trans. Amer. Math. Soc. 91, 102–112 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  3. Atneosen, G.A.: On the embeddability of compacta in n-books: intrinsic and extrinsic properties. PhD thesis, Michigan State University (1968)

  4. Bergman G.: Simplicial complexes with lattice structures. Algebr. Geom. Topol. 17, 439–486 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  5. García, O.C., Taylor, W.: The lattice of interpretability types of varieties. Mem. Amer. Math. Soc. 305 (1984)

  6. Lawson J.D., Madison B.: Peripherality in semigroups. Semigroup Forum 1, 128–142 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lawson J.D., Madison B.: Peripheral and inner points. Fund. Math. 69, 253–266 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lea J.W. Jr.: The peripherality of irreducible elments of a semigroup. Pacific J. Math. 45, 555–560 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  9. Neumann W.D.: On Mal’cev conditions. J. Aust. Math. Soc. 17, 376–384 (1974)

    Article  MATH  Google Scholar 

  10. Persinger C.A.: Subsets of n-books in E3. Pacific J. Mathematics 18, 169–173 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  11. Taylor, W.: The clone of a topological space. Res. Exp. Math. 13, Heldermann, Berlin (1986)

  12. Taylor W.: Spaces and equations. Fund. Math. 164, 193–240 (2000)

    MathSciNet  MATH  Google Scholar 

  13. Taylor W.: Equations on real intervals. Algebra Universalis 55, 409–456 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Taylor W.: Simple equations on real intervals. Algebra Universalis 61, 213–226 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Taylor, W.: Approximate satisfaction of identities. (2010 preprint) http://arXiv.org/abs/1504.01165

  16. Taylor, W.: Discontinuities in the identical satisfaction of equations. (2011 preprint) http://arXiv.org/abs/1504.01445

  17. Taylor, W. : Possible classification of finite-dimensional compact Hausdorff topological algebras. In: Don Pigozzi on Abstract Algebraic Logic and Universal Algebra. Forthcoming volume of Outstanding Contributions to Logic, Springer http://math.colorado.edu/~wtaylor/classify.pdf.

  18. Wikipedia: Book embeddings (2015), https://en.wikipedia.org/wiki/Book_embedding.

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, University of Colorado, Boulder, CO, 80309-0395, USA

    Walter Taylor

Authors
  1. Walter Taylor
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Walter Taylor.

Additional information

Presented by M. Ploscica.

I wish to thank George Bergman for valuable discussion in the preparation of this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Taylor, W. Compatibility of book-spaces with certain identities. Algebra Univers. 78, 601–612 (2017). https://doi.org/10.1007/s00012-017-0478-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00012-017-0478-4

2010 Mathematics Subject Classification

Key words and phrases

Search

Navigation