# On a characterization of the unit interval in terms of clones

Commentationes Mathematicae Universitatis Carolinae (1999)

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

## Access Full Article

top## Abstract

top## How to cite

topBarkhudaryan, 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

top- García O.C., Taylor W., The lattice of interpretability types of varieties, Mem. Amer. Math. Soc. 50 305 (1984). (1984) MR0749524
- Grätzer G., Universal algebra, 2-nd ed. Springer-Verlag Berlin and New York (1979). (1979) MR0538623
- Herrlich H., On the concept of reflection in general topology, Conf. on Contributions to Extension Theory of Topological Structures Berlin (1967). (1967)
- Herrlich H., Topologische Reflexionen und Coreflexionen, Lecture Notes in Math. 78 Springer-Verlag Berlin Heidelberg New York (1968). (1968) Zbl0182.25302MR0256332
- Kuratowski K., Topologie I, II, Monogr. Mat. Warsaw (1950). (1950)
- Lawvere F.W., Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869-872. (1963) Zbl0119.25901MR0158921
- Neumann W.N., On Malcev conditions, J. Austral. Math. Soc. 17 (1974), 376-384. (1974) Zbl0294.08004MR0371781
- Pultr A., Trnková V., Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North-Holland Amsterdam (1980). (1980) MR0563525
- Sichler J., Trnková V., On elementary equivalence and isomorphism of clone segments, Period. Math. Hungar. 32 (1996), 113-128. (1996) MR1407914
- Taylor W., The Clone of a Topological Space, Res. Exp. Math. 13 Heldermann Verlag (1986). (1986) Zbl0615.54013MR0879120
- Trnková V., Semirigid spaces, Trans. Amer. Math. Soc. 343 1 (1994), 305-325. (1994) MR1219734

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.