Three-space properties in paratopological gyrogroups

In this paper, we consider the three-space properties in paratopological gyrogroups. The fol-lowing are the established conclusions: (1) metrizability of compact (resp., sequentially compact, countably compact) subsets is a three-space property in the class of k-gentle paratopological gyrogroups; (2) let G be a strongly paratopological gyrocommutative gyrogroup and let H be a second-countable invariant topo-logical subgyrogroup of G. If the paratopological gyrogroup G/H has a countable network, then so does G; (3) let H be a compact strongly L-subgyrogroup of a paratopological gyrogroup G. If H and G/H have countable tightness, then G has countable tightness.