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New posts in separation-axioms
$f,g$ continuous from $X$ to $Y$. if they are agree on a dense set $A$ of $X$ then they agree on $X$
general-topology
continuity
separation-axioms
Why are ordered spaces normal? [collecting proofs]
general-topology
big-list
lattice-orders
separation-axioms
order-topology
Let $X,Y$ be Hausdorff and $f,g : X \to Y$ continuous. Let $A \subset X$ be dense and suppose that $f\mid_A = g\mid_A$. Show that $f=g$.
general-topology
continuity
solution-verification
separation-axioms
The set of points where two maps agree is closed?
general-topology
continuity
separation-axioms
$X/{\sim}$ is Hausdorff if and only if $\sim$ is closed in $X \times X$
general-topology
quotient-spaces
separation-axioms
How to prove that a compact set in a Hausdorff topological space is closed?
general-topology
compactness
separation-axioms
Why is this quotient space not Hausdorff?
general-topology
topological-groups
quotient-spaces
separation-axioms
Does this property characterize a space as Hausdorff?
general-topology
separation-axioms
$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
general-topology
separation-axioms
product-space
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