Celebratio Mathematica — Kuperberg — Complete Bibliography

Complete Bibliography

Works connected to William Raoul Reagle Transue

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K. Kuperberg, W. Kuperberg, and W. R. R. Transue: “On the 2-homogeneity of Cartesian products,” Fund. Math. 110 : 2 (1980), pp. 131–134. Dedicated to the memory and Ralph Bennett. MR 600586 Zbl 0475.54025 article

Włodzimierz Kuperberg	Related
William Raoul Reagle Transue	Related
Ralph Blount Bennett	Related

K. M. Kuperberg, W. Kuperberg, and W. R. R. Transue: “Homology separation and 2-homogeneity,” pp. 287–295 in Continua (Cincinnati, OH, 12–15 January 1994). Edited by H. Cook, W. T. Ingram, K. T. Kuperberg, A. Lelek, and P. Minc. Lecture Notes in Pure and Applied Mathematics 170. Dekker (New York), 1995. MR 1326851 Zbl 0826.54026 incollection

The homology separation axiom is introduced to investigate homogeneity properties of Cartesian products of continua. We prove that under certain conditions of a homological nature the products are factorwise rigid. Also, if the product \( X\times Y \) of an \( n \)-dimensional representable continuum \( X \) and a non-degenerate continuum \( Y \) is 2-homogeneous, then \( X \) is locally \( n \)-acyclic. In particular, the product \( B\times Y \) of a \( \mu^n \)-manifold \( B \) (based on the \( n \)-dimensional Menger universal compactum \( \mu^n \)) with any non-degenerate continuum \( Y \) is not 2-homogeneous. These theorems generalize a previous result of the same authors and some results of J. Kennedy Phelps.

Włodzimierz Kuperberg	Related
Howard Cook	Related
William Raoul Reagle Transue	Related
William Thomas Ingram, III	Related
Andrew Lelek	Related
Piotr Minc	Related