What is a continuous extension? - Mathematics Stack Exchange To find examples and explanations on the internet at the elementary calculus level, try googling the phrase "continuous extension" (or variations of it, such as "extension by continuity") simultaneously with the phrase "ap calculus" The reason for using "ap calculus" instead of just "calculus" is to ensure that advanced stuff is filtered out
is bounded linear operator necessarily continuous? 3 This property is unrelated to the completeness of the domain or range, but instead only to the linear nature of the operator Yes, a linear operator (between normed spaces) is bounded if and only if it is continuous