Sequences and nets


by ForMyThunder
Tags: nets, sequences
ForMyThunder
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#1
Jan5-11, 10:12 PM
P: 152
Say the real numbers were given a topology [tex]\left\{R,\phi, [0,1]\right\}[/tex]. Does the sequence (1/n) converge to every point of [0,1] since it is a neighborhood of every point?
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Jan6-11, 09:00 AM
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What is [itex]R[/itex] and [itex]\phi[/itex]? Does your topology satisfy the definition of a topology?
micromass
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Jan6-11, 10:22 AM
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If [tex]\mathbb{R}[/tex] has the topology [tex]\{\emptyset,[0,1],\mathbb{R}\}[/tex], then the sequence (1/n) converges to every point of [tex]\mathbb{R}[/tex]!

ForMyThunder
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#4
Jan6-11, 08:50 PM
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Sequences and nets


Quote Quote by micromass View Post
If [tex]\mathbb{R}[/tex] has the topology [tex]\{\emptyset,[0,1],\mathbb{R}\}[/tex], then the sequence (1/n) converges to every point of [tex]\mathbb{R}[/tex]!
Yeah, I guess you're right. Thanks.


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