Clone properties of topological spaces

Věra Trnková

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 4, page 427-440
  • ISSN: 0044-8753

Abstract

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Clone properties are the properties expressible by the first order sentence of the clone language. The present paper is a contribution to the field of problems asking when distinct sentences of the language determine distinct topological properties. We fully clarify the relations among the rigidity, the fix-point property, the image-determining property and the coconnectedness.

How to cite

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Trnková, Věra. "Clone properties of topological spaces." Archivum Mathematicum 042.4 (2006): 427-440. <http://eudml.org/doc/249796>.

@article{Trnková2006,
abstract = {Clone properties are the properties expressible by the first order sentence of the clone language. The present paper is a contribution to the field of problems asking when distinct sentences of the language determine distinct topological properties. We fully clarify the relations among the rigidity, the fix-point property, the image-determining property and the coconnectedness.},
author = {Trnková, Věra},
journal = {Archivum Mathematicum},
keywords = {finite products; clone; first order language; rigidity; fix-point property; image-determining property; coconnectedness; finite products; clone; first order language; rigidity},
language = {eng},
number = {4},
pages = {427-440},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Clone properties of topological spaces},
url = {http://eudml.org/doc/249796},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Trnková, Věra
TI - Clone properties of topological spaces
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 4
SP - 427
EP - 440
AB - Clone properties are the properties expressible by the first order sentence of the clone language. The present paper is a contribution to the field of problems asking when distinct sentences of the language determine distinct topological properties. We fully clarify the relations among the rigidity, the fix-point property, the image-determining property and the coconnectedness.
LA - eng
KW - finite products; clone; first order language; rigidity; fix-point property; image-determining property; coconnectedness; finite products; clone; first order language; rigidity
UR - http://eudml.org/doc/249796
ER -

References

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  1. Adámek J., Herrlich H., Strecker G., Abstract and Concrete Categories, Wiley–Interscience, New York 1990. (1990) MR1051419
  2. Brower L. E. J., On continuous one-to-one transformations of surfaces into themselves, Proc. Kon. Nederl. Akad. Wetensch. 11 (1909), 788–798. (1909) 
  3. Cook H., Continua which admit only the identity mapping onto non-degenerate sub-continua, Fund. Math. 60 (1967), 241–249. (1967) MR0220249
  4. Engelking R., General Topology, Państwowe Wydawnictvo Naukowe, Warszawa 1977. (1977) Zbl0373.54002MR0500779
  5. Garcia O. C., Taylor W., The lattice of interpretability of varieties, Mem. Amer. Math. Soc., No. 305 50 (1984). (1984) MR0749524
  6. Hall P., Some word problems, J. London Math. Soc. 33 (1958), 482–496. (1958) Zbl0198.02902MR0102540
  7. Herrlich H., On the concept of reflections in general topology, Proc. Symp. On extension theory of topological structures, Berlin 1967. (1967) 
  8. Herrlich H., Topologische Reflexionen und Coreflexionen, Lecture Notes in Math. 78 (1968), Springer-Verlag Berlin - Heidelberg - New York. (1968) Zbl0182.25302MR0256332
  9. Kuratowski C., Topologie I, II, Monografie Matematyczne, Warszaw 1950. (1950) 
  10. Lawvere F. W., Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U. S. A. 50 (1963), 869–872. (1963) Zbl0119.25901MR0158921
  11. Lawvere F. W., Some algebraic problems in context of functorial semantics of algebraic theories, Lecture Notes in Math. 61 (1968), 41–46, Springer-Verlag, Berlin and New York. (1968) MR0231882
  12. McKenzie R. N., McNulty G. F., Taylor W. F., Algebras, Lattices, Varieties, Vol. 1, Brooks/Cole, Monterey, California, 1978. (1978) 
  13. Pultr A., Trnková V., Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North Holland and Academia, Praha, 1980. (1980) MR0563525
  14. Sichler J., Trnková V., Maps between a space and its square, Topology Appl. 142 (2004), 159–179. Zbl1068.54009MR2071300
  15. Szendrei Á., Clones in Universal Algebra, Press de l’Université de Montréal, 1986. (1986) Zbl0603.08004MR0859550
  16. Taylor W., The Clone of a Topological Space, Research and Exposition Math. Vol 13, Helderman Verlag, 1986. (1986) Zbl0615.54013MR0879120
  17. Taylor W., Abstract Clone Theory, In: Algebras and Order, Proceedings of the NATO Advanced Study Institute, Montréal 1991 (I. G. Rosenberg and G. Sabidussi, eds.), Kluwer Academic Publishers (1993), 507–530. (1991) MR1233798
  18. Trnková V., Semirigid spaces, Trans. Amer. Math. Soc. 343 (1994), 305–329. (1994) MR1219734
  19. Trnková V., Co-connected spaces, Serdica Math. J. 24 (1998), 25–36. (1998) Zbl0940.54028MR1679189
  20. Trnková V., Clones, coclones and coconnected spaces, Acta Math. Univ. Commenianae 69 (2000), 241–259. Zbl1027.54016MR1819525
  21. Trnková V., Counting cocomponents of a topological space, Applied Categ. Structures 12 (2004), 379–396. Zbl1067.54004MR2094462

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