ArticleOriginal scientific text

Title

Embeddings of chains into chains

Authors 1, 1

Affiliations

  1. 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

Bibliography

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  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 2 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 τ and τ², (in Czech), Časopis Pěst. Mat. 78 (1953), 59-60.
Pages:
5-21
Main language of publication
English
Received
2005-04-18
Accepted
2005-05-30
Published
2005
Exact and natural sciences