Definition:Continuous Real Function/Half Open Interval
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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 $a$.
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 9.1$