Category:Theory of continuous functions

• Continuous function

A

• Absolute continuity
• Approximately continuous function
• Arzelà–Ascoli theorem

B

• Banach–Mazur theorem
• Banach–Stone theorem
• Blancmange curve
• Borsuk–Ulam theorem
• Bounded operator
• Brouwer fixed-point theorem
• Bundle map

C

• Classification of discontinuities
• Cliquish function
• Continuous functions on a compact Hausdorff space
• Continuous linear operator
• Continuous wavelet transform

D

• Darboux's theorem (analysis)
• Degree of a continuous mapping
• Direct image functor
• Direct image with compact support
• Direction-preserving function
• Discontinuities of monotone functions

E

• Equicontinuity

G

• Graph continuous function

H

• Heine–Cantor theorem
• Hemicontinuity
• Homeomorphism
• Homotopy

I

• Intermediate value theorem
• Invariance of domain

L

• Lefschetz fixed-point theorem
• Leray spectral sequence
• Local boundedness
• Local diffeomorphism
• Local homeomorphism
• Loop theorem

M

• Maximum theorem
• Metric map
• Michael selection theorem
• Microcontinuity
• Minkowski's question-mark function

N

• Normal family

O

• Open and closed maps

P

• Pasting lemma
• Peano curve
• Perfect map
• Proper map

Q

• Quasi-continuous function
• Quillen adjunction
• Quotient space (topology)

R

• Runge's phenomenon

S

• Semi-continuity
• Simplicial approximation theorem
• Space-filling curve
• Stone–Weierstrass theorem
• Symmetrically continuous function

T

• Tietze extension theorem

U

• Uniform continuity
• Urysohn's lemma

W

• Weierstrass function
• Weierstrass Nullstellensatz