Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
A space in which every two points can be joined by a continuous path.
wp-path-connectednlab-path-connectedhatcher-algebraic-topologyEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Every nonempty contractible space is path-connected.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-contractiblenlab-contractiblewp-path-connectednlab-path-connectedhatcher-algebraic-topologyThis is an authored directed relation from the source endpoint to the target endpoint.
Require every two points to be joined by a path.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-path-connectednlab-path-connectedhatcher-algebraic-topologyEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Every path-connected space is connected.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-path-connectednlab-path-connectedwp-connected-spacenlab-connected-spacetopology-without-tearsThis is an authored directed relation from the source endpoint to the target endpoint.
Require trivial fundamental group.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-simply-connectednlab-simply-connectedhatcher-algebraic-topology