Vol. 39, No. 3, 1971

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Concerning web-like continua

John Walter Hinrichsen

Vol. 39 (1971), No. 3, 691–694

The compact metric continuum M is said to be a web if and only if there exist two monotone upper semi-continuous decompositions G1 and G2 of M such that M∕G1 and M∕G2 are arcs and each element of G1 intersects each element of G2. It is shown that there exists in Euclidean 3-space a compact continuum M that is not a web but does have two monotone upper semicontinuous decompositions G1 and G2 such that (1) M∕G1 and M∕G2 are simple closed curves and (2) each element of G1 intersects each element of G2. Such continua are called pseudo-webs.

Mathematical Subject Classification 2000
Primary: 54F15
Received: 15 April 1970
Revised: 1 June 1971
Published: 1 December 1971
John Walter Hinrichsen