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1 Introduction 1

2 Generalized metrizable properties and cardinal invariants in paratopological and semitopological groups 7

2.1 First-countable paratopological groups and quasitopological groups 7

2.1.1 First-countable paratopological groups 8

2.1.2 First-countable quasitopological groups 11

2.2 Submetrizability of paratopological and semitopological groups 20

2.2.1 Submetrizability of paratopological groups 21

2.2.2 Submetrizability of semitopological groups 30

2.3 Mappings between paratopological groups 37

2.4 Cardinal invariants 41

2.5 Open problems 50

3 Remainders of paratopological and semitopological groups 53

3.1 Dichotomy theorems 54

3.2 Remainders for topological groups 61

3.3 Remainders for paratopological groups 68

3.3.1 Remainders being Lindel？f spaces 68

3.3.2 Remainders with a Gδ-diagonal 72

3.4 The remainders of semitopological groups 78

3.5 Open problems 83

4 R-factorizable topological groups 85

4.1 ω-uniform continuity in uniform spaces 86

4.2 ω-uniform continuity in topological groups 89

4.3 Characterization of R-factorizable topological groups 90

4.4 Characterization of m-factorizable groups 97

5 Factorization properties of paratopological groups 101

5.1 Notation and preliminary facts 102

5.2 Characterizing R-factorizable paratopological groups 104

5.3 R-factorizability in totally LΣ-groups 114

5.4 Open problems 121

Bibliography 123