# Sequences and nets

1. Jan 5, 2011

### ForMyThunder

Say the real numbers were given a topology $$\left\{R,\phi, [0,1]\right\}$$. Does the sequence (1/n) converge to every point of [0,1] since it is a neighborhood of every point?

Last edited: Jan 5, 2011
2. Jan 6, 2011

### Fredrik

Staff Emeritus
What is $R$ and $\phi$? Does your topology satisfy the definition of a topology?

3. Jan 6, 2011

### micromass

Staff Emeritus
If $$\mathbb{R}$$ has the topology $$\{\emptyset,[0,1],\mathbb{R}\}$$, then the sequence (1/n) converges to every point of $$\mathbb{R}$$!

4. Jan 6, 2011

### ForMyThunder

Yeah, I guess you're right. Thanks.