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by jason1996
Sat Nov 12, 2016 9:08 pm
Forum: General Topology
Topic: Continuous map
Replies: 2
Views: 3152

Re: Continuous map

We suppose that $ x_{n}\rightarrow x_{0}$. The set $ \left \{ x_{1},x_{2},.... \right.\left. \right \}\cup \left \{ x_{0} \right.\left.\right \}$ is compact and from the hypothesis(the restriction of f in every compact set is continuous) we obtain that $ f(x_{n})\rightarrow f(x_{0})$. So the proof h...
by jason1996
Sat Nov 12, 2016 4:50 pm
Forum: Number theory
Topic: Subset of natural numbers
Replies: 2
Views: 1999

Re: Subset of natural numbers

Suppose that is no $ n\in \mathbb{N}$, n>1 which divides every element of S. Then there exist $ a,b\in S$ with (a,b)=1. It is trivial to prove that for every $ k,l\in \mathbb{N}$, $ ka+lb\in S$. Let q>ab. Then if (k,l) solution of the equation ka+lb=q (1) there is either k>b or l>a.(2) Also we notic...