On minimal complexes

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An K-complex K is called p.w.l. minimal in Ed if each proper subcomplex of K is p.W.L. is embeddable in Ed. The main purpose of this paper is to prove that for each n ≧ 2, and each d9 n + 1 ≧ d ≧ 2n, there are countably many nonhomeomorphic N-complexes, each one of which is p.W.L. minimal in Ed and is not p.W.L. embeddable there. From general position arguments it follows that if an N-complex K is P.W.L. minimal in E2n, then for each x∈ |K|, |K| − {x} is embeddable topologicallyin E2n; if an N-complex K is p.W.L. minimal in En+d and is not embeddable there, then the dimension of each maximal simplex of K is at least d.

Original languageEnglish
Pages (from-to)721-727
Number of pages7
JournalPacific Journal of Mathematics
Issue number3
StatePublished - Mar 1969
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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