On Continua Whose Links Are Non-intersecting
نویسندگان
چکیده
There are many examples known of compact continua no two of whose simple links intersect, even though uncountably many of the links are nondegenerate. On page 346 of his Foundations of point set theory [ l] , R. L. Moore has given an example of a compact continuum which is the sum of an uncountable collection of nondegenerate simple links, only a countable number of which intersect. In view of these results it seems natural to inquire whether there is a compact continuum which is the sum of an uncountable collection of mutually exclusive nondegenerate simple links. Theorem 1 gives a negative answer. If we do not require that the continuum be compact, but do require that it be a separable locally connected Moore space, then Theorem 7 shows that the answer is again negative. References to theorem and page numbers refer to Moore's book, to which the reader is directed for definitions not given here.
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