STAR-COUNTABLE k-NETWORKS, COMPACT-COUNTABLE k-NETWORKS, AND RELATED RESULTS

In the theory of generalized metric spaces, the notion of knetworks has played an important role. Every locally separable metric space or CW-complex, more generally, every space dominated by locally separable metric spaces has a star-countable k-network. Every LaSnev space, as well as, every space dominated by LaSnev spaces has a a-compact-finite knetwork. We recall that every space has a compact-countable k-network if it has a star-countable k-network, a o-hereditarily closure preserving knetwork, or a a-compact-finite k-network, We investigate around spaces with a star-countable k-network, or a compact-countable k-network.