A Note on Paracompactness in Generalized Ordered Spaces

a) X is strongly paracompact; b) X is paracompact; c) X is metacompact; d) X is weakly θ-refinable; e) Every open cover of X has a point-countable open refinement; f) X is subparacompact; g) If C is a closed subspace of X, then there are discrete closed sets S and T which are, respectively, well-ordered and reverse-well-ordered by the given ordering of X, have S ∪ T ⊂ C, and have the property that if x ∈ C then some points s ∈ S and t ∈ T have s ≤ x ≤ t [F]; h) every gap and every pseudogap of X is a Q-gap [GH and L2]; i) no closed subspace of X is homeomorphic to a stationary subset of a regular uncountable cardinal.