Have you tried seeing the solutions on this site?
2000 Munkres # Topology: Solutions > Chapter 2 Topological Spaces and Continuous Functions » dbFin | dbFin
I'm having a lot of trouble understanding how to work a problem like this from topology...
Consider the product, uniform, and box topologies on R^{w} (that's an omega)
In which topologies do the following sequences converge?
w_{1} = (1,1,1,1,...)
w_{2} = (0,2,2,2,...)
w_{3} = (0,0,3,3,...)
...
x_{1} = (1,1,1,1,...)
x_{2} = (0,1/2,1/2,1/2,...)
x_{3} = (0,0,1/3,1/3,...)
...
y_{1} = (1,0,0,0,...)
y_{2} = (1/2,1/2,0,0,...)
y_{3} = (1/3,1/3,1/3,0...)
...
z_{1} = (1,1,0,0,...)
z_{2} = (1/2,1/2,0,0,...)
z_{3} = (1/3,1/3,0,0...)
...
Any help would be great...even just one set of the variables so I could have an example of where to go...Thanks!
Have you tried seeing the solutions on this site?
2000 Munkres # Topology: Solutions > Chapter 2 Topological Spaces and Continuous Functions » dbFin | dbFin