New posts in separation-axioms

Proving $R_L \times R_L$ is completely regular. Meaning $R_L \times R_L$ is an example of a space which is completely regular, but not normal

real-analysis general-topology separation-axioms product-space sorgenfrey-line

Topological groups are completely regular

topological-groups separation-axioms uniform-spaces

Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F

general-topology proof-writing proof-explanation separation-axioms

Show that any metrizable space $X$ is Hausdorff

general-topology metric-spaces proof-writing separation-axioms

$X$ normal $f:X \longrightarrow Y$ continuous, surjective, closed $\Longrightarrow$ $Y$ normal

general-topology separation-axioms closed-map

Study some topological properties of $I^{\aleph_0}\times I^2/M$

general-topology compactness connectedness separation-axioms path-connected

Image under covering map of Hausdorff space is Hausdorff?

general-topology covering-spaces separation-axioms

Why is $T_1$ required for a topological space to be $T_4$?

general-topology examples-counterexamples separation-axioms

Explain the argument used in the answer

general-topology solution-verification proof-explanation compactness separation-axioms

Normal space on $[ -1,1]$

general-topology analysis separation-axioms

Looking For a Neat Proof of the Fact that the Grassmannian Manifold is Hausdorff

general-topology differential-geometry quotient-spaces separation-axioms grassmannian

Topology on $\mathbb{R}$ strictly coarser (resp. finer) than the usual one which is still Hausdorff (resp. connected)

general-topology examples-counterexamples connectedness separation-axioms

A finite Hausdorff space is discrete

general-topology separation-axioms

Showing that the space is normal.(exercise) [duplicate]

general-topology separation-axioms closed-map

When is a quotient by closed equivalence relation Hausdorff

general-topology quotient-spaces separation-axioms

Are there any countable Hausdorff connected spaces?

general-topology examples-counterexamples connectedness separation-axioms

Does removing finitely many points from an open set yield an open set?

general-topology separation-axioms

Separation Axioms: is it true that $T_4 \Rightarrow T_3 \Rightarrow T_2 \Rightarrow T_1 \Rightarrow T_0$?

general-topology separation-axioms

Is it true that every normal countable topological space is metrizable?

general-topology metric-spaces examples-counterexamples separation-axioms

Let $U(a,t) = \{a\} \cup [t, \infty)$ where $a,t \in \Bbb R.$ Show that the generated space is not Hausdorff.

general-topology separation-axioms