I claim that if a function ##f:\mathbb{R}\rightarrow\mathbb{R}## is continuous at a point ##a##, then there exists a ##\delta>0## and ##|h|<\delta## such that ##f## is also continuous in the ##h##-neighbourhood of ##a##.
Please advice if my proof as follows is correct.
Continuity at ##a##...
Continuity at a point implies continuity in the neighborhood
Continuity at a point implies continuity in the neighborhood
Please advice if my proof as follows is correct.
Continuity at ##a##...
Continuity at a point implies continuity in the neighborhood
Continuity at a point implies continuity in the neighborhood
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