Cardinal invariants in locally Ti-minimal paratopological groups

In this paper, cardinal invariants in locally Ti-minimal paratopological groups with i=1,2,3 are studied. It mainly shows that: (1) If (G,τ) is a T2 locally T1-minimal 2-oscillating paratopological group, then χ(G)=πχ(G)⋅inv(G); (2) Let (G,τ) be a locally T1-minimal paratopological group, then χ(G)=ψ(G)⋅inv(G); (3) If (G,τ) is a locally T2-minimal paratopological group, then χ(G)=ψ(G)⋅inv(G)⋅Hs(G); (4) If (G,τ) is a locally T3-minimal paratopological group, then χ(G)=ψ(G)⋅inv(G)⋅Ir(G). These results generalize the corresponding results in [9] and also give positive answers to two questions posed by F.C. Lin in [9].