Continuity at a point implies continuity in the neighborhood

samedi 18 avril 2015

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

0 commentaires:

Enregistrer un commentaire