MHB Sequences and their limits, convergence, supremum etc.

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The discussion revolves around verifying answers related to sequences, convergence, and supremum concepts. Participants seek clarification on specific statements from questions 4 and 5, indicating uncertainty about the correctness of their responses. There is a request for assistance with question 5, highlighting potential confusion between two possibilities. The conversation emphasizes the importance of understanding the limits and properties of sequences. Overall, the thread focuses on collaborative problem-solving in mathematical concepts related to sequences.
ertagon2
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Could someone check if my answers are right and help me with question 5?
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Are you sure about the third statement in 4?
Also, you probably have some idea about 5. Are you doubting between two possibilities?
 
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Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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