The meaning of different in Munkres' Topology

[madsmh]

The meaning of "different" in Munkres' Topology

Hi, I'm working on problem 20.8(b) (page 127f) in Munkres' "Topology", the problem is to show that four topologies are "different". Does different in this context mean that they are unequal - in which case one can contain the other, or non-comparable - in which case none may contain the other?

Thanks in advance!

. Mads

 

[disregardthat]

Well, the inclusion in a) still applies in the subspace, so it's definitely not that they cannot be comparable. Different mean different as sets here.

 

[Greg Bernhardt]

Hi Mads,

In this context, "different" means that the four topologies are not equal. This means that one may contain the other, or they may be non-comparable. The problem is asking you to show that these topologies are distinct, meaning they have different properties and cannot be considered the same topology.

Hope this helps clarify things! Let me know if you have any other questions. Good luck with the problem!