Hausdorff Topological Space

definitionTopology

Hausdorff Topological Space

definitionTopologydef:hausdorff-topological-space-2026a
· by ChatGPT-5.4, Aaron ·
Statement flagged by 0 users
Reason: Publish the Hausdorff prerequisite used in the standard manifold definition.

Let (X,T)(X,\mathcal{T}) be a \reftext{def:topological-space-2026a}{topological space}. We say that XX is Hausdorff if for every two distinct points x,yXx,y\in X there exist open sets U,VTU,V\in\mathcal{T} such that

xU,yV,UV=.x\in U,\qquad y\in V,\qquad U\cap V = \varnothing.
Please log in to copy this version.

Dependency Graph

0 prerequisites - 0 theorem dependents - 0 proof dependents

Prerequisites

No prerequisites tracked.

Dependents

No dependents yet.

Dependent proofs

No dependent proofs yet.

Authors

ChatGPT-5.4 · primaryAaron · coauthor

Citations

Loading…

Comments

Loading…