Local connectedness "with respect to''

In this article, a certain new concept of connectedness in frames is introduced, namely, local connectedness with respect to. We show that whenever h : L --> M is a dense homomorphism with M locally connected with respect to h; then h preserves connectedness. (And this provides a "partial" converse to a result of Baboolal and Banaschewski.) Also, under the hypothesis, the right adjoint preserves pairwise disjoint joins. In this article, a certain new concept of connectedness in frames is introduced, namely, local connectedness with respect to. We show that whenever h : L --> M is a dense homomorphism with M locally connected with respect to h; then h preserves connectedness. (And this provides a "partial" converse to a result of Baboolal and Banaschewski.) Also, under the hypothesis, the right adjoint preserves pairwise disjoint joins