Thread: Topology: product, uniform, and box topology converging sequences

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?
w₁ = (1,1,1,1,...)
w₂ = (0,2,2,2,...)
w₃ = (0,0,3,3,...)
...
x₁ = (1,1,1,1,...)
x₂ = (0,1/2,1/2,1/2,...)
x₃ = (0,0,1/3,1/3,...)
...
y₁ = (1,0,0,0,...)
y₂ = (1/2,1/2,0,0,...)
y₃ = (1/3,1/3,1/3,0...)
...
z₁ = (1,1,0,0,...)
z₂ = (1/2,1/2,0,0,...)
z₃ = (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