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- W1600260649 abstract "An open cover of a topological space is said to be an $omega$âcover if there is for each finite subset of the space a member of the cover which contains the finite set, but the space itself is not a member of the cover. We prove theorems which imply that a set $X$ of real numbers has Rothbergerâs property $textsf {C}^{prime prime }$ if, and only if, for each positive integer $k$, for each $omega$âcover $mathcal {U}$ of $X$, and for each function $f:[mathcal {U}]^2rightarrow {1,dots ,k}$ from the two-element subsets of $mathcal {U}$, there is a subset $mathcal {V}$ of $mathcal {U}$ such that $f$ is constant on $[mathcal {V}]^2$, and each element of $X$ belongs to infinitely many elements of $mathcal {V}$ (Theorem 1). A similar characterization is given of Mengerâs property for sets of real numbers (Theorem 6)." @default.
- W1600260649 created "2016-06-24" @default.
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- W1600260649 date "1999-01-01" @default.
- W1600260649 modified "2023-10-16" @default.
- W1600260649 title "Open covers and partition relations" @default.
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- W1600260649 doi "https://doi.org/10.1090/s0002-9939-99-04513-x" @default.
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