# Category:Definitions/Connected Spaces

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This category contains definitions related to Connected Spaces in the context of Topology.

Related results can be found in Category:Connected Spaces.

Let $T = \struct {S, \tau}$ be a non-empty topological space.

$T$ is **connected** if and only if there exists no continuous surjection from $T$ onto a discrete two-point space.

## Subcategories

This category has the following 10 subcategories, out of 10 total.

### A

- Definitions/Arc-Connected Spaces (14 P)

### C

- Definitions/Connected Sets (16 P)

### D

### I

- Definitions/Irreducible Spaces (13 P)

### L

### P

### U

## Pages in category "Definitions/Connected Spaces"

The following 27 pages are in this category, out of 27 total.

### C

- Definition:Connected (Topology)
- Definition:Connected (Topology)/Points
- Definition:Connected (Topology)/Topological Space
- Definition:Connected (Topology)/Topological Space/Definition 1
- Definition:Connected (Topology)/Topological Space/Definition 2
- Definition:Connected (Topology)/Topological Space/Definition 3
- Definition:Connected (Topology)/Topological Space/Definition 4
- Definition:Connected (Topology)/Topological Space/Definition 5
- Definition:Connected (Topology)/Topological Space/Definition 6
- Definition:Connected (Topology)/Topological Space/Definition 7
- Definition:Connected Between Two Points
- Definition:Connected Manifold
- Definition:Connected Points (Topology)
- Definition:Connected Subspace
- Definition:Connected Topological Space
- Definition:Cut Point