Abstract: | Let {X i , π k i , ω} be an inverse sequence and $X = \mathop {\lim }\limits_ \leftarrow \left\{ {X_i ,\pi _k^i ,\omega } \right\}$ . If each X i is hereditarily (resp. metaLindelöf, σ-metaLindelöf, σ-orthocompact, weakly suborthocompact, δθ-refinable, weakly θ-refinable, weakly δθ-refinable), then so is X. |