Rigid pairs of long arcs
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- by Gary G. Miller PDF
- Proc. Amer. Math. Soc. 31 (1972), 591-594 Request permission
Abstract:
Arcs (linearly ordered continua) $A$ and $B$ are constructed such that every map from $A$ to $B$ and every map from $B$ to $A$ is constant. The Generalized Continuum Hypothesis is sufficient for the existence of two such arcs each of cardinality ${2^\aleph }$ for each uncountable cardinal $\aleph$.References
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- M. A. Maurice, Compact ordered spaces, Mathematical Centre Tracts, vol. 6, Mathematisch Centrum, Amsterdam, 1964. MR 0220252 G. Miller Jumps and gaps in lexicographic products (to appear).
- V. Novák, On the lexicographic dimension of linearly ordered sets, Fund. Math. 56 (1964), 9–20. MR 207597, DOI 10.4064/fm-56-1-9-20
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 591-594
- DOI: https://doi.org/10.1090/S0002-9939-1972-0290336-2
- MathSciNet review: 0290336