ON r-REGULAR CONVERGENCE
نویسندگان
چکیده
In his paper On sequences and limiting sets [ l ] , 1 G. T. Whyburn introduced the notion of regular convergence. He showed that in the cases of 0 and 1 regular convergence (see definition below) that the limit of sequences of many simple topological sets is of the same type as the members of the sequence. I t is the purpose of this paper to extend some of these results to higher dimensions. The lack of simple characterizations of the higher dimension sets (such as the ^-sphere) makes the results much weaker than in the 0 and 1 dimensional cases. It is assumed throughout the paper that all sets lie in a compact metric space. All our complexes and cycles will be non-oriented, and the Vietoris cycles and chains ( F-cycles and F-chains) will have these as coordinates. The set of all points x whose distance from a set A is less than e will be denoted by U€(A). Finally we shall denote the boundary of an r-dimensional complex (or F-chain) z by z>
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