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Co-elementary equivalence, co-elementary maps, and generalized arcs
Author(s):
Paul
Bankston
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3715-3720.
MSC (1991):
Primary 03C20, 54B35, 54C10, 54D05, 54D30, 54D80, 54F05, 54F15
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Abstract:
By a generalized arc we mean a continuum with exactly two non-separating points; an arc is a metrizable generalized arc. It is well known that any two arcs are homeomorphic (to the real closed unit interval); we show that any two generalized arcs are co-elementarily equivalent, and that co-elementary images of generalized arcs are generalized arcs. We also show that if  is a function between compacta and if  is an arc, then  is a co-elementary map if and only if  is an arc and  is a monotone continuous surjection.
References:
- 1.
- B. Banaschewski, ``More on compact Hausdorff spaces and finitary duality,'' Can. J. Math. 36(1984), 1113-1118. MR 86h:18002
- 2.
- P. Bankston, ``Reduced coproducts of compact Hausdorff spaces,'' J. Symbolic Logic 52(1987), 404-424. MR 88k:54021
- 3.
- -------, ``Model-theoretic characterizations of arcs and simple closed curves,'' Proc. A. M. S. 104(1988), 898-904. MR 89m:03023
- 4.
- ------, ``Co-elementary equivalence for compact Hausdorff spaces and compact abelian groups,'' J. Pure and Applied Algebra 68 (1990), 11-26. MR 91k:03095
- 5.
- -------, ``Taxonomies of model-theoretically defined topological properties,'' J. Symbolic Logic 55(1990), 589-603. MR 91g:03065
- 6.
- -------, ``On the topological model theory of normal disjunctive lattices,'' (submitted)
- 7.
- C. C. Chang and H. J. Keisler, ``Model Theory (Third Edition),'' North Holland, Amsterdam, 1989. MR 91c:03026
- 8.
- P. Eklof, ``Ultraproducts for algebraists,'' in ``Handbook of Mathematical Logic,'' North Holland, Amsterdam, 1977, pp. 105-137.
- 9.
- R. Gurevi\v{c}, ``On ultracoproducts of compact Hausdorff spaces,'' J. Symbolic Logic 53(1988), 294-300. MR 89b:03051
- 10.
- J. G. Hocking and G. S. Young, ``Topology,'' Addison-Wesley, Reading, MA, 1961. MR 23:A2857
- 11.
- J. Nikiel, H. M. Tuncali, and E. D. Tymchatyn, ``Continuous images of arcs and inverse limit methods,'' Memoirs of the A. M. S. 104 (no. 498) (1993), 1-80. MR 94a:54084
- 12.
- J. Rosický, ``Categories of models,'' Seminarberichte Mathematik Informatik Fernuniversität 19(1984), 337-413.
- 13.
- H. Wallman, ``Lattices and topological spaces,'' Ann. Math.(2) 39(1938), 112-126.
- 14.
- S. Willard, ``General Topology,'' Addison-Wesley, Reading, MA, 1970. MR 41:9173
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Additional Information:
Paul
Bankston
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisconsin 53201-1881
Email:
paulb@mscs.mu.edu
DOI:
10.1090/S0002-9939-97-04088-4
PII:
S 0002-9939(97)04088-4
Keywords:
Ultraproduct,
ultracoproduct,
generalized arc,
co-elementary equivalence,
co-elementary map
Received by editor(s):
July 2, 1996
Communicated by:
Andreas R. Blass
Copyright of article:
Copyright
1997,
American Mathematical Society
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