Sequences and nets

ForMyThunder

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?

Fredrik

What is [itex]R[/itex] and [itex]\phi[/itex]? Does your topology satisfy the definition of a topology?

micromass

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

Quote by micromass

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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ForMyThunder	Sequences and nets Tweet 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?

Fredrik Mentor	What is [itex]R[/itex] and [itex]\phi[/itex]? Does your topology satisfy the definition of a topology?

micromass Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus	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]!