Sequences and Nets: Does (1/n) Converge to [0,1]?

[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?

 

[Fredrik]

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

 

[micromass]

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

 

[ForMyThunder]

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

Yeah, I guess you're right. Thanks.