Sequences and nets

by ForMyThunder
Tags: nets, sequences
 P: 152 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?
 Emeritus Sci Advisor PF Gold P: 8,863 What is $R$ and $\phi$? Does your topology satisfy the definition of a topology?
 Mentor P: 15,911 If $$\mathbb{R}$$ has the topology $$\{\emptyset,[0,1],\mathbb{R}\}$$, then the sequence (1/n) converges to every point of $$\mathbb{R}$$!
P: 152

Sequences and nets

 Quote by micromass 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.

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