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I was wondering if anyone knew of a name for such a set, namely a subset [itex]S \subseteq \mathbb{R}^n[/itex] which at every point [itex]x \in S[/itex] there exists

**no**open subset [itex]U[/itex] of [itex]\mathbb{R}^n[/itex] containing [itex]x[/itex] such that [itex]S \cap U[/itex] is homeomorphic to either [itex]\mathbb{R}^m[/itex] or the half-space [tex]\mathbb{H}^m = \{(y_1,...,y_m) \in \mathbb{R}^m : y_m \geq 0\}[/tex] for any integer [itex]m \geq 0[/itex]. Of course, any set for which such open sets [itex]U[/itex] exists for every [itex]x[/itex] is called an embedded manifold with boundary. I'm looking for the opposite notion, in a sense.
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