# Talk:Inner Limit in Normed Spaces by Open Balls

While it's conceptually simple ($\epsilon \mathcal B$ is just a unit ball where every element is multiplied by $\epsilon$, and therefore the same as an open $\epsilon$-ball), is there any reason to prefer it over $\mathcal B_\epsilon$? I ask because all the books I've seen use $\mathcal B_\epsilon$ (or a variant), and it is more straightforward to link to Definition:Open Ball where the concept is explained in detail rather than assume the knowledge of what $\epsilon \mathcal B$ is, or have to explain it each time it's used. Thoughts? --prime mover 09:50, 26 November 2011 (CST)
It is just one notational convention I'm using because I find it convenient. But it is equivalent to using $\mathcal{B}_\epsilon:=\left\{x|\left\|x\right\|<\epsilon\right\}\equiv \epsilon \mathcal{B}$. --Pantelis Sopasakis 11:43, 26 November 2011 (CST)