4. In the usual topology again, is locally compact? 5. Deduce. {(0, 0)} U {(x, y) = R²; x >0}
4. In the usual topology again, is locally compact? 5. Deduce. {(0, 0)} U {(x, y) = R²; x >0}
Elementary Linear Algebra (MindTap Course List)
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Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 56E: Give an example showing that the union of two subspaces of a vector space V is not necessarily a...
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topology part 4 5
![3. Deduce.
Exercise 3.
Let X be a locally compact space.
1. Show that every closed subspace in X is locally compact.
2. Show that if X is Hausdorff then every open subspace in X is locally compact.
3. In usual R2, say why {(0,0)} and {(x, y) = R²; x>0} are locally compact.
4. In the usual topology again, is
{(0,0)} U {(x, y) = R²; x>0}
locally compact?
5. Deduce.
Good Luck](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8765329c-fafe-4a03-a485-f0c3c6508324%2Fb2911639-920f-4477-9c2d-5b4391837d9a%2Fc1285kh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Deduce.
Exercise 3.
Let X be a locally compact space.
1. Show that every closed subspace in X is locally compact.
2. Show that if X is Hausdorff then every open subspace in X is locally compact.
3. In usual R2, say why {(0,0)} and {(x, y) = R²; x>0} are locally compact.
4. In the usual topology again, is
{(0,0)} U {(x, y) = R²; x>0}
locally compact?
5. Deduce.
Good Luck
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