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For this question a manifold-with-boundary is a topological space which is connected, Hausdorff, and locally half-spaceupper-Euclidean. Every metrizable manifold-with-boundary has a collared boundary, as shown in "Locally flat imbeddings of topological manifolds", Morton Brown, 1962. Let $M$ be a non-metrizable manifold-with-boundary. Does $M$ have a collared boundary?

For this question a manifold-with-boundary is a topological space which is connected, Hausdorff, and locally half-space-Euclidean. Every metrizable manifold-with-boundary has a collared boundary, as shown in "Locally flat imbeddings of topological manifolds", Morton Brown, 1962. Let $M$ be a non-metrizable manifold-with-boundary. Does $M$ have a collared boundary?

For this question a manifold-with-boundary is a topological space which is Hausdorff and locally upper-Euclidean. Every metrizable manifold-with-boundary has a collared boundary, as shown in "Locally flat imbeddings of topological manifolds", Morton Brown, 1962. Let $M$ be a non-metrizable manifold-with-boundary. Does $M$ have a collared boundary?

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Collared boundary of a non-metrizable manifold

For this question a manifold-with-boundary is a topological space which is connected, Hausdorff, and locally half-space-Euclidean. Every metrizable manifold-with-boundary has a collared boundary, as shown in "Locally flat imbeddings of topological manifolds", Morton Brown, 1962. Let $M$ be a non-metrizable manifold-with-boundary. Does $M$ have a collared boundary?