This question is related to [one of previous questions.](https://mathoverflow.net/questions/312803/is-there-a-generalized-order-space-x-with-countable-tightness-which-is-not-fir) 


For any generalized order space $X$, $X$ has countable tightness iff $X$ is first countable.


Since a generalized order space is monotonically normal, the following question is natural.



> 
> Is there a monotonically normal space $X$ with countable tightness which is not first countable?
> 
> 
> 


thanks a lot!



A question on monotonically normal spaces
There are many examples. Take one ultrafilter $u$ on $\mathbb{N}$ and consider $\mathbb{N}\cup\{u\}$ as a subspace of $\beta\mathbb{N}$ (every point of $\mathbb{N}$ is isolated and the basic open neighbourhhods for $u$ are the sets of the form $U\cup\{u\}$ with $U\in u$). The resulting space has countable tightness but it is not first-countable at $u$.


The one-point compactification of an uncountable discrete space has countable tightness yet it does not even have countable pseudocharacter. 


