Further results on images of metric spaces

We introduce the notion of an ls-?-Ponomarev-system to give necessary and sufficient conditions for f:(M,M0) ? X to be a strong wc-mapping (wc-mapping, wk-mapping) where M is a locally separable metric space. Then, we systematically get characterizations of weakly continuous strong wc-images (wc-images, wk-images) of locally separable metric spaces by means of certain networks. Also, we give counterexamples to sharpen some results on images of locally separable metric spaces in the literature.

L-Ponomarev system and images of locally separable metric spaces

We introduce the notion of an L-Ponomarev system (f,M,X, P*n), and give characterizations of certain msss-images (resp., mssc-images) of locally separable metric spaces. As an application, we get a new characterization of quotient msss-images (mssc-images) of locally separable metric spaces, which is helpful in solving Velichko?s question (1987).

Weak-open images of locally separable metric spaces

In this paper, we prove that a space X is a weak-open compact image of a locally separable metric space if and only if X has a uniform cosmic-weak-base if and only if X is a weak-open compact image of a metric space and a locally cosmic space, and give some internal characterizations of weak-open s-images of locally separable metric spaces.

On sequence-covering mssc-images of locally separable metric spaces

We characterize sequence-covering (resp., 1-sequence-covering, 2-sequence-covering) mssc-images of locally separable metric spaces by means of ?-locally finite cs-networks (resp., sn-networks, so-networks) consisting of ?0-spaces (resp., sn-second countable spaces, so-second countable spaces). As the applications, we get characterizations of certain sequence-covering, quotient mssc-images of locally separable metric spaces.

Onπ-Images of Locally Separable Metric Spaces

We characterizeπ-images of locally separable metric spaces by means of covers havingπ-property. As its application, we obtain characterizations of compact-covering (sequence-covering, pseudo-sequence-covering, and sequentially quotient)π-images of locally sparable metric spaces.