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- W2002201704 abstract "Let E and B be metric continua. Let p:E~>B be a shape fibration in the sense of Mardesic and Rushing. If B is arcwise connected, then all the fibers of p have the same shape. This is also true if B is connected by shape paths in the sense of Krasinkiewicz and Mine. It had been asked whether that this would be true without any assumptions other than B being a continuum. In this paper an example is given of a shape fibration p: E ~* B with E and B metric continua such that p has fibers of different shape. l Introductions. Let E — (En, hn) and B = (Bn, qn) be inverse sequences of metric compaeta. A level map piE-^B^ is a sequence of maps pn: En -» Bn such that for each n the following diagram commutes. If each pn is a fibration, we say that p is a level map of fibratίons. Each level map P'-E-^B^ induces a map p: E —> B between the inverse limits E = lim E and B — lim B. It is well-known that all the fibers of a fibration p: E —> B have the same homotopy type provided B is path wise connected. If p: E —> B is induced by a level map of fibrations (or more generally by a shape fibration in the sense of S. Mardesic and T. B. Rushing ([8] and [7])), and if B is pathwise connected, then any two fibers have the same shape. This is actually true more generally when B is connected by shape paths in the sense of J. Krasinkiewicz and P. Mine [6]. In this paper we show that one cannot strengthen this by assuming only that B is connected. More precisely we prove the following theorem." @default.
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- W2002201704 title "A shape fibration with fibers of different shape" @default.
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- W2002201704 doi "https://doi.org/10.2140/pjm.1979.84.319" @default.
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