Connected Space
A Space 
is connected if any two points in can be connected by a curve lying wholly within . ASpace is 0-connected (a.k.a. Pathwise-Connected) if every Map from a 0-Sphere to theSpace extends continuously to the 1-Disk. Since the 0-Sphere is the two endpoints of an interval(1-Disk), every two points have a path between them. A space is 1-connected (a.k.a. Simply Connected) ifit is 0-connected and if every Map from the 1-Sphere to it extends continuously to a Map from the2-Disk. In other words, every loop in the Space is contractible. A Space is 
-MultiplyConnected if it is 
-connected and if every Map from the -Sphere into it extends continuouslyover the 
-Disk.
A theorem of Whitehead says that a Space is infinitely connected Iff it is contractible.
See also Connectivity, Locally Pathwise-Connected Space, Multiply Connected, Pathwise-Connected,Simply Connected- Fisher Sign Test
- Fisher Skewness
- Fisher's Theorem
- Fisher's z-Distribution
- Fisher's z'-Transformation
- Fisher-Tippett Distribution
- Fitting Subgroup
- Five Cubes
- Five Disks Problem
- Five Tetrahedra Compound
- Fixed
- Fixed Element
- Fixed Point
- Fixed Point (Differential Equations)
- Fixed Point (Map)
- Fixed Point Theorem
- Fixed Point (Transformation)
- Flag
- Flag Manifold
- Flat
- Flat Norm
- Flat Space Theorem
- Flat Surface
- Flattening
- Flemish Knot