Scrabble?! MONOTONICALLY

Definitions of MONOTONICALLY in various dictionaries:

In mathematics, a monotonically normal space is a particular kind of normal space, with some special characteristics, and is such that it is hereditarily normal, and any two separated subsets are strongly separated. They are defined in terms of a monotone normality operator. A T 1 {\displaystyle T_{1}} topological space ( X , T ) {\displaystyle (X,{\mathcal {T}})} is said to be monotonically normal if the following condition holds: For every x ∈ G {\displaystyle x\in G} , where G is open, there is an open set μ ( x , G ) {\displaystyle \mu (x,G)} such that x ∈ μ ( x , G ) ⊆ G {\displaystyle x\in \mu (x,G)\subseteq G} if μ ( x , G ) ∩ μ ( y , H ) ≠ ∅ {\displaystyle \mu (x,G)\cap \mu (y,H)\neq \emptyset } then either x ∈ H {\displaystyle x\in H} or y ∈ G {\displaystyle y\in G} .There are some equivalent criteria of monotone normality.