Remainders for a class of quotients of paratopological groups

The metrizability conditions and cardinal invariants for compactly-fibered coset spaces in paratopological groups in terms of their remainders are considered. It mainly shows that: (1) Suppose that X is a quotient of a k-gentle paratopological group with respect to a compact subgroup; then the remainder Y of X is either pseudocompact or Lindelöf; (2) Suppose that X is a quotient of paratopological group with respect to a compact subgroup with a remainder Y such that Y has a point-countable base; then X and Y are separable and metrizable; (3) Suppose that X is a quotient of paratopological group with respect to a compact subgroup with a remainder Y such that Y is weakly developable; then nw(X)=πw(X)=πw(Y)=ω. Many results on coset spaces of topological groups obtained by A.V. Arhangel'skiı̌ [5] are extended to coset spaces of paratopological groups.