Full Idea
Cantor's conjecture (the Continuum Hypothesis) is that there are no sets between N and P(N). The 'generalized' version replaces N with an arbitrary infinite set.
Clarification
'N' is the natural numbers, and 'P(N)' is their power set
Gist of Idea
Continuum Hypothesis: there are no sets between N and P(N)
Source
report of George Cantor (works [1880]) by Robert S. Wolf - A Tour through Mathematical Logic 2.2
Book Reference
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.67
A Reaction
The initial impression is that there is a single gap in the numbers, like a hole in ozone layer, but the generalised version implies an infinity of gaps. How can there be gaps in the numbers? Weird.