# interior and closure of a set in sequence space

• February 20th 2011, 07:20 AM
hermanni
interior and closure of a set in sequence space
Let A = { $( x_{n} ) : \sum_{n=1}^{\infty} | x_{n} | \leq 1$ } Find the interior and the closure of A in $c_{0}$. Here $c_{0} =$ { $(x_{n}) \in R : x_{n} -> 0$ } i.e space of all sequences that converges to 0.
Can anyone help, any hint is appreciated. (Thinking)
• February 21st 2011, 12:19 AM
hermanni
Metric is the usual sup metric i.e. $d( x_{n} , y_{n} ) = sup_{k} | x_{k} - y_{k} |$