# Definition talk:Continuous Real Function/Left-Continuous

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I enforced $S$ to be open to avoid trivial cases (eg. isolated points, left end-point of closed interval). Arguably these need be incorporated as trivial extensions; just give me a heads up if this is indeed desired, and I will adapt the statement. --Lord_Farin 11:27, 5 April 2012 (EDT)

Also, when time and need come, I will generalise this to only require a topology on the codomain, instead of it being $\R$. The domain needs to be $\R$ to sensibly speak about 'left', 'right' and 'limit' (well, maybe $\Q$, but $\overline{\R}$ has trouble at the infties). --Lord_Farin 11:30, 5 April 2012 (EDT)