On a characterization of the unit interval in terms of clones

Artur Barkhudaryan

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 1, page 153-164
  • ISSN: 0010-2628

Abstract

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This paper gives a partial solution to a problem of W. Taylor on characterization of the unit interval in the class of all topological spaces by means of the first order properties of their clones. A characterization within the class of compact spaces is obtained.

How to cite

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Barkhudaryan, Artur. "On a characterization of the unit interval in terms of clones." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 153-164. <http://eudml.org/doc/248430>.

@article{Barkhudaryan1999,
abstract = {This paper gives a partial solution to a problem of W. Taylor on characterization of the unit interval in the class of all topological spaces by means of the first order properties of their clones. A characterization within the class of compact spaces is obtained.},
author = {Barkhudaryan, Artur},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {clones of topological spaces; algebraic theories; unit interval; clone of a topological space; unit interval},
language = {eng},
number = {1},
pages = {153-164},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a characterization of the unit interval in terms of clones},
url = {http://eudml.org/doc/248430},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Barkhudaryan, Artur
TI - On a characterization of the unit interval in terms of clones
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 1
SP - 153
EP - 164
AB - This paper gives a partial solution to a problem of W. Taylor on characterization of the unit interval in the class of all topological spaces by means of the first order properties of their clones. A characterization within the class of compact spaces is obtained.
LA - eng
KW - clones of topological spaces; algebraic theories; unit interval; clone of a topological space; unit interval
UR - http://eudml.org/doc/248430
ER -

References

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  4. Herrlich H., Topologische Reflexionen und Coreflexionen, Lecture Notes in Math. 78 Springer-Verlag Berlin Heidelberg New York (1968). (1968) Zbl0182.25302MR0256332
  5. Kuratowski K., Topologie I, II, Monogr. Mat. Warsaw (1950). (1950) 
  6. Lawvere F.W., Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869-872. (1963) Zbl0119.25901MR0158921
  7. Neumann W.N., On Malcev conditions, J. Austral. Math. Soc. 17 (1974), 376-384. (1974) Zbl0294.08004MR0371781
  8. Pultr A., Trnková V., Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North-Holland Amsterdam (1980). (1980) MR0563525
  9. Sichler J., Trnková V., On elementary equivalence and isomorphism of clone segments, Period. Math. Hungar. 32 (1996), 113-128. (1996) MR1407914
  10. Taylor W., The Clone of a Topological Space, Res. Exp. Math. 13 Heldermann Verlag (1986). (1986) Zbl0615.54013MR0879120
  11. Trnková V., Semirigid spaces, Trans. Amer. Math. Soc. 343 1 (1994), 305-325. (1994) MR1219734

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