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ON SUBSETS OF THE PARTITION R IN THE NUMERICAL STRAIGHT LINE R

Wei Guo (Xi'an College of Geology)  
A space X partitions a space Y" means that there is a family of embeddings of X into Y, so that the images form a cover of Y by pairwise disjoint sets ( symbol XY ) .In this paper, some partial solutions are given to the question raised by Bankston-McGovern[1] . The main results are as follows: ( 1 ) If M is a nonempty subset of R, o-dimensional, then MR; ( 2 ) If U is an open subset of R, U≠φ, then UR and only U is an open interval; ( 3 ) If F is a closed subset of R, 1-dimentional, then FR, only F has an unbounded domponent C, and ( F/C1 ) is closed.
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