On resolvability and tightness in uncountable spaces

We investigate connections between resolvability and different forms of tightness. This study is adjacent to 1, 2. We construct a non-regular refinement ^* of the natural topology of the real line R with properties such that the space (R, ^*) has a hereditary nowhere dense tightness and it has no ₁-resolvable subspaces, whereas (R, ^*) = c. We also show that the proof of the main result of 1, being slightly modified, leads to the following strengthening: if L is a Hausdorff space of countable character and the space L^ is c. c. c. , then every submaximal dense subspace of L^ has disjoint tightness. As a corollary, for every there is a Tychonoff submaximal space X such that |X|= (X) = and X has disjoint tightness.