In order for convenience in checking definition along learning in Math, I found it necessary to gather definitions of the same kind so that distinguishing the differences among them will no longer be a tedious job. This work is very hard to do even many materials are available, if you want to use for commercial use, please contact me for permission. Furthermore, the work is still long from finished, if you want to contribute for more or better definitions, please contact me.

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### 1. Continuous at a point

#### Definition

#### Reference

None

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## 2. Pointwise Continuous

#### Definition

#### Reference

None

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## 3. Uniformly Continuous

#### Definition

#### Reference

None

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## 4. Continuous(of linear functions)

#### Definition

#### Reference

Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter I

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- Theorems/Corollary/Propositions/Lemmas

## 5. Continuous(of bilinear form)

#### Definition

#### Reference

Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter V

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- Theorems/Corollary/Propositions/Lemmas

## 6. Equicontinuous

#### Definition

#### Reference

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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- Theorems/Corollary/Propositions/Lemmas

## 8. Continuous relative to a subset

#### Definition

#### Reference

Convex Analysis Rockafellar RT, Chapter2, Section10

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- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 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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- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 10. Upper Semi Continuous(u.s.c.)

#### Definition

#### Reference

Convex Analysis Rockafellar RT, Chapter2, Section7

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## 11. Continuous from below(of measures)

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 2 Section 9

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## 12. Continuous from above(of measures)

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 2 Section 9

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## 13. Absolutely Continuous(of measures)

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 5 Section 23

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## 14. Uniformly Absolutely Continuous(of measures)

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 5 Section 24

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- Theorems/Corollary/Propositions/Lemmas

## 15. Absolutely Continuous(of signed measures)

#### Definition

#### Remark

#### Reference

Measure Theory, Paul R. Halmos, Chapter 6 Section 30

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas