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Discussiones Mathematicae General Algebra and Applications 25(1) (2005) 5-21
DOI: https://doi.org/10.7151/dmgaa.1090

EMBEDDINGS OF CHAINS INTO CHAINS

Vítězslav Novák and Tomáš Novotný

Masaryk University, Faculty of Education
Poříčí 31, 603 00 Brno, Czech Republic

Abstract

Continuity of isotone mappings and embeddings of a chain G into another chain are studied. Especially, conditions are found under which the set of points of discontinuity of such a mapping is dense in G.

Keywords: chain, cut, isotone mapping, embedding, continuity, dense subset.

2000 Mathematics Subject Classification: 06A05, 06F30.

References

[1]	G. Birkhoff, Generalized arithmetics, Duke Math. J. 9 (1942), 283-302.
[2]	G. Birkhoff, Lattice Theory, 3rd edition, Amer. Math. Soc., Providence, RI, 1967.
[3]	F. Hausdorff, Grundzüge der Mengenlehre, Leipzig 1914 (reprinted in: Chelsea Publ. Co., New York 1978).
[4]	S. Kurepa, Peano's transformations and Suslin's problem, (in Serbo-Croatian), Glasnik Mat.- Fiz. Astr. Ser. II 8 (1953), 175-190.
[5]	J. Novák, On some ordered continua of power 2Ŕ0 containing a dense subset of power Ŕ1, Czechoslovak Math. J.1 (76) (1951), 63-79.
[6]	M. Novotný, On similarity of ordered continua of types t and t2, (in Czech), Časopis Pěst. Mat. 78 (1953), 59-60.

Received 18 April 2003

Revised 30 May 2005