Hello :) i have a question on topology:
Let X be locally compact and Hausdorff. I want to prove the following: If $Y\subset X$ is open then Y is locally compact.
How to prove this? I have prove this for closed subsets. Also i want to conculude with this two lemmas that the following holds:
If $Y\subset X$ is locally closed then Y is locally compact.
Can somesone help me?! Thank you