Characterizing polyhedrons and manifolds
Commentationes Mathematicae Universitatis Carolinae (2003)
- Volume: 44, Issue: 4, page 711-725
- ISSN: 0010-2628
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Abstract
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topBarkhudaryan, Artur. "Characterizing polyhedrons and manifolds." Commentationes Mathematicae Universitatis Carolinae 44.4 (2003): 711-725. <http://eudml.org/doc/249160>.
@article{Barkhudaryan2003,
abstract = {In [5], W. Taylor shows that each particular compact polyhedron can be characterized in the class of all metrizable spaces containing an arc by means of first order properties of its clone of continuous operations. We will show that such a characterization is possible in the class of compact spaces and in the class of Hausdorff spaces containing an arc. Moreover, our characterization uses only the first order properties of the monoid of self-maps. Also, the possibility of characterizing the closed unit interval of the real line and some related objects in the category of partially ordered sets and monotonous maps will be illustrated.},
author = {Barkhudaryan, Artur},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {monoids of continuous maps; clones; compact space; monoid of continuous maps; clone},
language = {eng},
number = {4},
pages = {711-725},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Characterizing polyhedrons and manifolds},
url = {http://eudml.org/doc/249160},
volume = {44},
year = {2003},
}
TY - JOUR
AU - Barkhudaryan, Artur
TI - Characterizing polyhedrons and manifolds
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 4
SP - 711
EP - 725
AB - In [5], W. Taylor shows that each particular compact polyhedron can be characterized in the class of all metrizable spaces containing an arc by means of first order properties of its clone of continuous operations. We will show that such a characterization is possible in the class of compact spaces and in the class of Hausdorff spaces containing an arc. Moreover, our characterization uses only the first order properties of the monoid of self-maps. Also, the possibility of characterizing the closed unit interval of the real line and some related objects in the category of partially ordered sets and monotonous maps will be illustrated.
LA - eng
KW - monoids of continuous maps; clones; compact space; monoid of continuous maps; clone
UR - http://eudml.org/doc/249160
ER -
References
top- Barkhudaryan A., On a characterization of the unit interval in terms of clones, Comment. Math. Univ. Carolinae 40 (1999), 1 153-164. (1999) Zbl1060.54512MR1715208
- Kuratowski K., Topologie I, II, Monogr. Mat., Warsaw, 1950.
- Magill K.D., Jr., Subbiah S., Green's relations for regular elements of semigroups of endomorphisms, Canad. J. Math. 26 (1974), 6 1484-1497. (1974) Zbl0316.20041MR0374309
- Sichler J., Trnková V., On elementary equivalence and isomorphism of clone segments, Period. Math. Hungar. 32 (1-2) (1996), 113-128. (1996) MR1407914
- Taylor W., The Clone of a Topological Space, Res. Exp. Math. 13, Heldermann Verlag, 1986. Zbl0615.54013MR0879120
- Trnková V., Semirigid spaces, Trans. Amer. Math. Soc. 343 (1994), 1 305-325. (1994) MR1219734
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