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Keywords:
finite products; clone; first order language; rigidity; fix-point property; image-determining property; coconnectedness
finite products; clone; first order language; rigidity; fix-point property; image-determining property; coconnectedness
Summary:
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.
References:
[1] Adámek J., Herrlich H., Strecker G.: Abstract and Concrete Categories. Wiley–Interscience, New York 1990. MR 1051419
[2] Brower L. E. J.: On continuous one-to-one transformations of surfaces into themselves. Proc. Kon. Nederl. Akad. Wetensch. 11 (1909), 788–798.
[3] Cook H.: Continua which admit only the identity mapping onto non-degenerate sub-continua. Fund. Math. 60 (1967), 241–249. MR 0220249
[4] Engelking R.: General Topology. Państwowe Wydawnictvo Naukowe, Warszawa 1977. MR 0500779 | Zbl 0373.54002
[5] Garcia O. C., Taylor W.: The lattice of interpretability of varieties. Mem. Amer. Math. Soc., No. 305 50 (1984). MR 0749524
[6] Hall P.: Some word problems. J. London Math. Soc. 33 (1958), 482–496. MR 0102540 | Zbl 0198.02902
[7] Herrlich H.: On the concept of reflections in general topology. Proc. Symp. On extension theory of topological structures, Berlin 1967.
[8] Herrlich H.: Topologische Reflexionen und Coreflexionen. Lecture Notes in Math. 78 (1968), Springer-Verlag Berlin - Heidelberg - New York. MR 0256332 | Zbl 0182.25302
[9] Kuratowski C.: Topologie I, II. Monografie Matematyczne, Warszaw 1950.
[10] Lawvere F. W.: Functorial semantics of algebraic theories. Proc. Nat. Acad. Sci. U. S. A. 50 (1963), 869–872. MR 0158921 | Zbl 0119.25901
[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. MR 0231882
[12] McKenzie R. N., McNulty G. F., Taylor W. F.: Algebras, Lattices, Varieties. Vol. 1, Brooks/Cole, Monterey, California, 1978.
[13] Pultr A., Trnková V.: Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories. North Holland and Academia, Praha, 1980. MR 0563525
[14] Sichler J., Trnková V.: Maps between a space and its square. Topology Appl. 142 (2004), 159–179. MR 2071300 | Zbl 1068.54009
[15] Szendrei Á.: Clones in Universal Algebra. Press de l’Université de Montréal, 1986. MR 0859550 | Zbl 0603.08004
[16] Taylor W.: The Clone of a Topological Space. Research and Exposition Math. Vol 13, Helderman Verlag, 1986. MR 0879120 | Zbl 0615.54013
[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. MR 1233798
[18] Trnková V.: Semirigid spaces. Trans. Amer. Math. Soc. 343 (1994), 305–329. MR 1219734
[19] Trnková V.: Co-connected spaces. Serdica Math. J. 24 (1998), 25–36. MR 1679189 | Zbl 0940.54028
[20] Trnková V.: Clones, coclones and coconnected spaces. Acta Math. Univ. Commenianae 69 (2000), 241–259. MR 1819525 | Zbl 1027.54016
[21] Trnková V.: Counting cocomponents of a topological space. Applied Categ. Structures 12 (2004), 379–396. MR 2094462 | Zbl 1067.54004
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