On the covering and the additivity number of the real line
On the covering and the additivity number of the real line
We show that the real line <italic>R</italic> cannot be covered by <italic>k</italic> many nowhere dense sets iff <italic>whenever</italic> <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D equals StartSet upper D Subscript i Baseline colon i element-of k EndSet"> <mml:semantics> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>D</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:mrow> …