- #1
davidebianco1
- 2
- 0
Hello Everyone,
first of all my apologies, may be my question is too stupid for a forum on Topology and Geometry, but it's something I was thinking about for a while without getting an answer : What's the actual difference between a Close set and a Complete set? I mean : from an algebraic point of view, we say that a Close set contains the limits of its successions, whereas a complete set contains the limits of its Cauchy successions. But we can show that a succession is convergent if and only if it is a Cauchy succession, so the two concepts should be equivalent, and I don't see the difference between closure and completeness. From a topological point of view, we define a close set as the complement of an open one, but at this point I don't see the connection with the completeness property. I started to taught the actual difference could be in passing from infinite dimension to finite dimension, but I am not able to see clearly why. Can anyone help me?
Sorry again if the question is not so relevant. Cheers,
Davide
first of all my apologies, may be my question is too stupid for a forum on Topology and Geometry, but it's something I was thinking about for a while without getting an answer : What's the actual difference between a Close set and a Complete set? I mean : from an algebraic point of view, we say that a Close set contains the limits of its successions, whereas a complete set contains the limits of its Cauchy successions. But we can show that a succession is convergent if and only if it is a Cauchy succession, so the two concepts should be equivalent, and I don't see the difference between closure and completeness. From a topological point of view, we define a close set as the complement of an open one, but at this point I don't see the connection with the completeness property. I started to taught the actual difference could be in passing from infinite dimension to finite dimension, but I am not able to see clearly why. Can anyone help me?
Sorry again if the question is not so relevant. Cheers,
Davide