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1. Continuous at a point
Definition
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2. Pointwise Continuous
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3. Uniformly Continuous
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4. Continuous(of linear functions)
Definition
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Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter I
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5. Continuous(of bilinear form)
Definition
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Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter V
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6. Equicontinuous
Definition
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Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter IV
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7. Uniformly Equicontinuous
Definition
Competitive Definition
Reference
Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter IV(Definition)
Convex Analysis Rockafellar RT, Chapter2, Section10(Competitive Definition)
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8. Continuous relative to a subset
Definition
Reference
Convex Analysis Rockafellar RT, Chapter2, Section10
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9. Lower Semi Continuous(l.s.c.)
Definition
Competitive Definition
Properties
Reference
Convex Analysis Rockafellar RT, Chapter2, Section7(Definition)
Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter I(Competitive Definition, Properties)
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10. Upper Semi Continuous(u.s.c.)
Definition
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Convex Analysis Rockafellar RT, Chapter2, Section7
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11. Continuous from below(of measures)
Definition
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Measure Theory, Paul R. Halmos, Chapter 2 Section 9
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12. Continuous from above(of measures)
Definition
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Measure Theory, Paul R. Halmos, Chapter 2 Section 9
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13. Absolutely Continuous(of measures)
Definition
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Measure Theory, Paul R. Halmos, Chapter 5 Section 23
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14. Uniformly Absolutely Continuous(of measures)
Definition
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Measure Theory, Paul R. Halmos, Chapter 5 Section 24
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15. Absolutely Continuous(of signed measures)
Definition
Remark
Reference
Measure Theory, Paul R. Halmos, Chapter 6 Section 30
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