| Quasitopological groups and paratopological groups are important generalizations of topological groups.This thesis mainly studies the properties of reflections of quasitopological groups and s-paratopological groups.In Chapter 2,we study the reflections of quasitopological groups,and obtain the characterizations of Ti-reflections（i∈{1,2}）for quasitopological groups,and construct a quasitopological group G such that T1(T3（G）≠T3（T1（G））.Using the general stability theorems,many properties P are invariants or inverse invariants of φG,i for i∈{1,2} in the category of quasitopological groups.Chapter 3 investigates the properties of s-paratopological groups.We first prove that the class of s-paratopological groups is closed with finite products by a constructive method,and is closed with open subgroups.The s-coreflections of paratopological groups are defined,and an internal characterization of s-coreflection of paratopological groups is obtained by using sequentially open subsets.Then,we consider a special class of s-paratopological groups,that is the s-paratopological groups are determined by PT-sequences,we show that this class of paratopological groups is closed with finite products,and give a characterization that two T-sequences define the same paratopological group topologies in Abelian groups.Finally,the s-sums of Abelian s-paratopological groups are defined,and characterizations of s-paratopological groups and Hausdorff s-paratopological groups are obtained by using the s-sums.More precisely:（G,τ）is an s-paratopological group if and only if every continuous sequence-covering homomorphism from an s-paratopological group onto（G,τ）is quotient;A Hausdorff paratopological group is an s-paratopological group if and only if（G,τ）is a quotient group of the s-sums of a nonempty family of copies of（Z0ω;τe）. |
