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**MHB**members,

I have a quick question as follows.

Let $I$ be a compact interval and $\Omega$ denote the set of functions $f:I\to\mathbb{R}$,

which has at most finite number of discontinuities on $I$ such that if $t$ is a discontinuity point of $f$, then $\lim_{\tau\to t^{+}}f(\tau)=f(t)$ and $\lim_{\tau\to t^{-}}f(\tau)$ exists.

Is $\Omega$ a Banach space?

Thanks.

**bkarpuz**