Remarks on Certain Pathological Open Subsets of 3-space and Their Fundamental Groups
نویسنده
چکیده
We shall consider several well known subsets of spherical 3-space 5: the compact zero-dimensional set P described by Antoine [l]1 and the topological 3-cell C consisting of the "horned sphere" 2 of Alexander [2] together with its interior. That the fundamental groups, tti(S-P) and 7Ti(5— C), of their complementary domains are not finitely generated (and hence in particular not trivial) was noted by Alexander [2, pp. 9 and 11]. It is the main purpose of this note to give a
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