Timeline for Does every locally compact Hausdorff space admit a locally finite open covering by relatively compact sets?
Current License: CC BY-SA 4.0
8 events
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| S Mar 27, 2023 at 18:40 | history | suggested | Steven Clontz | CC BY-SA 4.0 |
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| Mar 27, 2023 at 18:07 | review | Suggested edits | |||
| S Mar 27, 2023 at 18:40 | |||||
| Apr 26, 2015 at 20:39 | comment | added | Mirko | @Corbennick My counterexample no longer works as the answerer corrected condition 2, replacing countable union with disjoint union. | |
| Apr 26, 2015 at 20:11 | history | edited | Joseph Van Name | CC BY-SA 3.0 |
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| Apr 26, 2015 at 13:50 | comment | added | user1688 | Here is a proof that 3 implies 1: Let $(V_i)$ be any open covering and $(U_j)$ a locally finite one by relatively compacts. Then each $U_j$ can be covered by finetely many $V_i$. Replace each $U_j$ by the finietely many intersections with those $V_i$ and you found a locally finite refinement of $(V_i)$. | |
| Apr 26, 2015 at 13:45 | comment | added | user1688 | I agree that 1 and 3 are equivalent, but condition 2 is out of place here as Mirko gave a counterexample. | |
| Apr 25, 2015 at 21:48 | history | edited | Joseph Van Name | CC BY-SA 3.0 |
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| Apr 25, 2015 at 20:45 | history | answered | Joseph Van Name | CC BY-SA 3.0 |