In fact now I see that an even simpler counterexample is the discrete topology on any X of positive dimension.
12.
In the case of topologies, the greatest element is the discrete topology and the least element is the trivial topology.
13.
In discrete group theory, where " G " has the discrete topology, a simpler definition is used.
14.
Compact groups are a natural generalisation of finite groups with the discrete topology and have properties that carry over in significant fashion.
15.
There are some occasions when a topological group or Lie group is usefully endowed with the discrete topology,'against nature '.
16.
Equivalently, a connection is flat if the structure group can be reduced to the same underlying group but with the discrete topology.
17.
The greatest element in this fiber is the discrete topology on " X " while the least element is the indiscrete topology.
18.
That is if X \ backslash \ { p \ } has the discrete topology then the open extension topology will be the excluded point topology.
19.
This also defines a metric, but gives a completely different topology, the " discrete topology "; with this definition numbers cannot be arbitrarily close.
20.
A group algebra has an identity, as opposed to just an approximate identity, if and only if the topology on the group is the discrete topology.
