# Definition:Continuous Real Function/Half Open Interval

## Definition

Let $f$ be a real function defined on a half open interval $\hointl a b$.

Then $f$ is continuous on $\hointl a b$ if and only if it is:

$(1): \quad$ continuous at every point of $\openint a b$
$(2): \quad$ continuous on the left at $b$.

Let $f$ be a real function defined on a half open interval $\hointr a b$.

Then $f$ is continuous on $\hointr a b$ if and only if it is:

$(1): \quad$ continuous at every point of $\openint a b$
$(2): \quad$ continuous on the right at $a$.