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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)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
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
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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