# Category:Continuous Mappings

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This category contains results about continuous mappings in the context of Topology.

## Subcategories

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

### C

### H

### U

## Pages in category "Continuous Mappings"

The following 79 pages are in this category, out of 79 total.

### B

### C

- Combination Theorem for Continuous Mappings
- Compactness is Preserved under Continuous Surjection
- Compactness Properties Preserved under Continuous Surjection
- Compactness Properties Preserved under Projection Mapping
- Complex-Differentiable Function is Continuous
- Composite of Continuous Mappings is Continuous
- Composite of Continuous Mappings is Continuous/Point
- Composite of Continuous Mappings on Metric Spaces is Continuous
- Constant Function is Continuous
- Constant Mapping is Continuous
- Continuity Defined by Closure
- Continuity Defined from Closed Sets
- Continuity from Union of Restrictions
- Continuity of Composite with Inclusion
- Continuity of Composite with Inclusion/Inclusion on Mapping
- Continuity of Composite with Inclusion/Mapping on Inclusion
- Continuity of Composite with Inclusion/Uniqueness of Induced Topology
- Continuity of Mapping between Metric Spaces by Closed Sets
- Continuity Test using Basis
- Continuity Test using Sub-Basis
- Continuous Bijection from Compact to Hausdorff is Homeomorphism
- Continuous Bijection from Compact to Hausdorff is Homeomorphism/Corollary
- Continuous Image of Connected Space is Connected
- Continuous Image of Connected Space is Connected/Corollary 2
- Continuous Involution is Homeomorphism
- Continuous Mapping from Compact Space to Hausdorff Space Preserves Local Connectedness
- Continuous Mapping is Continuous on Induced Topological Spaces
- Continuous Mapping is Measurable
- Continuous Mapping is Sequentially Continuous
- Continuous Mapping is Sequentially Continuous/Corollary
- Continuous Mapping of Separation
- Continuous Mapping on Finite Union of Closed Sets
- Continuous Mapping on Union of Open Sets
- Continuous Mapping to Topological Product
- Continuous Mapping to Topological Product/Corollary
- Countability Axioms Preserved under Open Continuous Surjection
- Countability Properties Preserved under Projection Mapping
- Countable Compactness is Preserved under Continuous Surjection