If $(X,\tau)$ is a connected space, then $\tau$ [need not be contained in a maximal connected topology](https://mathoverflow.net/questions/201477/maximal-connected-topologies).


Is the Euclidean topology on $\mathbb{R}$ contained in a maximal connected topology?



Is the Euclidean topology on $\mathbb{R}$ contained in a maximal connected topology?
Yes, see *[Maximal connected expansions of the reals](https://doi.org/10.1090/S0002-9939-1978-0467646-4)* by J. A. Guthrie, H. E. Stone and M. L. Wage, *Proc. Amer. Math. Soc. 69 (1978), 159-165.* 


