
#1
Jan511, 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?




#2
Jan611, 09:00 AM

Emeritus
Sci Advisor
PF Gold
P: 9,017

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




#3
Jan611, 10:22 AM

Mentor
P: 16,701

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]!




#4
Jan611, 08:50 PM

P: 152

Sequences and nets 


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