# Category:Definitions/Continuity

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This category contains definitions related to continuity, in all its various contexts.

Related results can be found in Category:Continuity.

The mapping $f$ is **continuous at (the point) $x$** (with respect to the topologies $\tau_1$ and $\tau_2$) if and only if:

## Subcategories

This category has the following 5 subcategories, out of 5 total.

### A

### C

### P

## Pages in category "Definitions/Continuity"

The following 80 pages are in this category, out of 80 total.

### C

- Definition:Continuity
- Definition:Continuity/Metric Subspace
- Definition:Continuous at Point of Metric Space
- Definition:Continuous at Point of Metric Space/Also known as
- Definition:Continuous at Point of Normed Vector Space
- Definition:Continuous at Point of Topological Space
- Definition:Continuous Extension
- Definition:Continuous Function
- Definition:Continuous Linear Transformation Space
- Definition:Continuous Mapping
- Definition:Continuous Mapping (Metric Space)
- Definition:Continuous Mapping (Metric Space)/Also known as
- Definition:Continuous Mapping (Metric Space)/Point
- Definition:Continuous Mapping (Metric Space)/Point/Definition 1
- Definition:Continuous Mapping (Metric Space)/Point/Definition 2
- Definition:Continuous Mapping (Metric Space)/Point/Definition 3
- Definition:Continuous Mapping (Metric Space)/Point/Definition 4
- Definition:Continuous Mapping (Metric Space)/Space
- Definition:Continuous Mapping (Metric Space)/Space/Definition 1
- Definition:Continuous Mapping (Metric Space)/Space/Definition 2
- Definition:Continuous Mapping (Normed Vector Space)
- Definition:Continuous Mapping (Normed Vector Space)/Point
- Definition:Continuous Mapping (Normed Vector Space)/Point/Definition 1
- Definition:Continuous Mapping (Normed Vector Space)/Space
- Definition:Continuous Mapping (Normed Vector Space)/Space/Definition 1
- Definition:Continuous Mapping (Topological Spaces)
- Definition:Continuous Mapping (Topology)
- Definition:Continuous Mapping (Topology)/Everywhere
- Definition:Continuous Mapping (Topology)/Everywhere/Open Sets
- Definition:Continuous Mapping (Topology)/Everywhere/Pointwise
- Definition:Continuous Mapping (Topology)/Point
- Definition:Continuous Mapping (Topology)/Point/Filters
- Definition:Continuous Mapping (Topology)/Point/Neighborhoods
- Definition:Continuous Mapping (Topology)/Point/Open Sets
- Definition:Continuous Mapping (Topology)/Set
- Definition:Continuous Mapping at Point (Topology)
- Definition:Continuous Mapping Between Topological Spaces at Point
- Definition:Continuous Mapping on Set
- Definition:Continuous on Metric Space
- Definition:Continuous Real Function
- Definition:Continuous Real-Valued Function
- Definition:Continuous Real-Valued Vector Function

### D

- Definition:Differentiability Class
- Definition:Discontinuity
- Definition:Discontinuity of the First Kind
- Definition:Discontinuous Mapping
- Definition:Discontinuous Mapping/Real Function
- Definition:Discontinuous Mapping/Real Function/Point
- Definition:Discontinuous Mapping/Topological Space
- Definition:Discontinuous Mapping/Topological Space/Point

### E

### L

- Definition:Lipschitz Condition
- Definition:Lipschitz Constant
- Definition:Lipschitz Continuity
- Definition:Lipschitz Continuity/Lipschitz Constant
- Definition:Lipschitz Continuity/Point
- Definition:Lipschitz Continuous at Point
- Definition:Lower Semicontinuous
- Definition:Lower Semicontinuous on Subset
- Definition:Lower Semicontinuous/Subset