### A topological duality for the $F$-chains associated with the logic ${C}_{\omega}$

In this paper we present a topological duality for a certain subclass of the ${F}_{\omega}$-structures defined by M. M. Fidel, which conform to a non-standard semantics for the paraconsistent N. C. A. da Costa logic ${C}_{\omega}$. Actually, the duality introduced here is focused on ${F}_{\omega}$-structures whose supports are chains. For our purposes, we characterize every ${F}_{\omega}$-chain by means of a new structure that we will call down-covered chain (DCC) here. This characterization will allow us to prove the dual equivalence between the...