Vol. 28, No. 3, 1969

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On minimal complexes

Joseph Zaks

Vol. 28 (1969), No. 3, 721–727

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

Mathematical Subject Classification
Primary: 57.01
Received: 14 May 1968
Published: 1 March 1969
Joseph Zaks