The equivalence of zero span and zero semispan

Davis, James Francis

doi:10.1090/S0002-9939-1984-0722431-3

The equivalence of zero span and zero semispan
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by James Francis Davis PDF

Proc. Amer. Math. Soc. 90 (1984), 133-138 Request permission

Abstract:

In this paper we introduce the idea of the symmetric span of a continuum, and show that continua with zero symmetric span are in class $W$. Continua with zero span have zero symmetric span, but the converse does not hold. We also show that if every subcontinuum of the continuum $M$ is in class $W$ then the span of $M$ and the semispan of $M$ agree. These results are then applied to show that the properties of having zero span and of having zero semispan are equivalent.

References

Edwin Duda and James Kell III, Two sum theorems for semispan, Houston J. Math. 8 (1982), no. 3, 317–321. MR 684158
J. B. Fugate, Decomposable chainable continua, Trans. Amer. Math. Soc. 123 (1966), 460–468. MR 196720, DOI 10.1090/S0002-9947-1966-0196720-1
W. T. Ingram, An atriodic tree-like continuum with positive span, Fund. Math. 77 (1972), no. 2, 99–107. MR 365516, DOI 10.4064/fm-77-2-99-107
W. T. Ingram, Decomposable circle-like continua, Fund. Math. 63 (1968), 193–198. MR 240786, DOI 10.4064/fm-63-2-193-198

Atriodic tree-like continua and the span of mappings

1

John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
A. Lelek, Disjoint mappings and the span of spaces, Fund. Math. 55 (1964), 199–214. MR 179766, DOI 10.4064/fm-55-3-199-214
A. Lelek, Some problems concerning curves, Colloq. Math. 23 (1971), 93–98, 176. MR 307204, DOI 10.4064/cm-23-1-93-98
A. Lelek, On the surjective span and semispan of connected metric spaces, Colloq. Math. 37 (1977), no. 1, 35–45. MR 482680, DOI 10.4064/cm-37-1-35-45
R. L. Moore, Foundations of point set theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR 0150722
R. H. Sorgenfrey, Concerning triodic continua, Amer. J. Math. 66 (1944), 439–460. MR 10968, DOI 10.2307/2371908