Abstract
Let M be a manifold modeled on a locally convex linear metric space E≌ E ω (or ≌ E ω f and N a Z-submanifold of M. Then N is collared in M. In this paper, we study the following problem [1, 3]: Under what conditions can M be embedded in E so that N is the topological boundary of M in E? We gain a more mild sufficient condition than the previous papers [7, 8] and a necessary and sufficient condition in the case M has the homotopy type of S n (and each component of N is simply connected if n⩾2) and in the case N has the homotopy type of S n ( n⩾2). Also we obtain a necessary and sufficient condition under which M can be embedded in E so that bd M = N and cl( E\\ M) has the homotopy type of S n (we assume that M and N are simply connected if n ⩾ 2).
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