TITLE: Name for topological spaces where "every point has a local base wellordered by reverse inclusion"?
QUESTION [7 upvotes]: There are many properties regarding local bases of a topological space, like first countable if every point has a countable local base. 
Is there a similar name for a space where "every point has a local base wellordered by reverse inclusion"? 
That is, given $X=(X,\tau)$ topological space, we say $X$ has the property if for every $x\in X$ there exists $\mathcal{B}=\{B_i\}_{i\in\kappa}\subset\tau$ such that $B_i\subset B_j$ for every $j<i<\kappa$.
Does this property have any known consequence or relation with other properties?

REPLY [9 votes]: Note that replacing "well-ordered" by "linearly-ordered" produces an equivalent property since any linear order contains a cofinal well order.
Such spaces were called lob-spaces and studied by S.W. Davis in Spaces with linearly ordered local bases, Topology proceedings 3, (1978), pp.37-51.