In this paper, we treat of an
E-manifold pair (
M,
N) with
N a Z-set in
M where
E is an infinite-dimensional locally convex linear metric space which is homeomorphic to
Eω or
Eωf. And we study the condition under which
M can be embedded in
E such that
N is the topological boundary under the embedding (Anderson's Problem in [2]). Moreover we extend the results on topological stability and deficiency, the Homeomorphism Extension Theorem and the results in [18].
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