Given a compact space $T^*$ and Hausdorff space $T$ on set $X$ such that $T^* \subseteq T$. Show that $T^*=T$
122663
Proving $T$ and $U$ are equal if I know $(X,T)$ and $(X,U)$ are hausdorff and compact
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
2667
Given $S \hookrightarrow T$ construct $U ≈ T$ disjoint from $S$ in Z set theory?
70785
A finite Hausdorff space is discrete
149426
Is there a Hausdorff space $X$ separating points of any Hausdorff space?
149220
If every compact set is closed, then is the space Hausdorff?
81488
If a continuous function$f: (X, \mathscr T_X) \to (Y, \mathscr T_Y)$ is injective (Given $Y$ is Hausdorff), show that X is hausdorff
78763
Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
39076
Contraction of compact sets
7069
On the product of $\mathfrak c$-many separable spaces
66334
How is every subset of the set of reals with the finite complement topology compact?
148112
Prove that a topological space equipped with a delta-complex structure is Hausdorff
22131
Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.
83166
Homeomorphism(topological spaces) version of Cantor–Bernstein–Schroeder theorem
28637
Proving continuous image of compact sets are compact
128457
Show that $T$ is a compact operator
141642
Closure of a certain subset in a compact topological group