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A function between topological spaces whose inverse image of every open set is open.
The inverse-image definition covers arbitrary topological spaces and is equivalent to the neighborhood formulation.
wp-continuous-functionnlab-continuous-maptopology-without-tearsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Fréchet differentiability at a point implies continuity there; a differentiable function is therefore continuous on its domain.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-differentiable-functionnlab-differentiable-mapThis is an authored directed relation from the source endpoint to the target endpoint.
Require inverse images of codomain-open sets to be open in the domain.
Feed several structures into a construction junction and impose compatibility between them.
wp-continuous-functionnlab-continuous-maptopology-without-tearsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the continuous map to be bijective and its inverse map to be continuous.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-homeomorphismnlab-homeomorphismtopology-without-tears