The disjoint union of metrizable spaces is metrizable.
33859
How to show that a disjoint sum of metric spaces is metrizable?
134859
Let $(X, \mathcal{T})$ be a metrizable space. Prove that $X$ Lindelöf implies that $X$ is separable.
142093
The closure of an irreducible subset of an irreducible space is irreducible.
70413
A vector space over $R$ is not a countable union of proper subspaces
101986
Prob. 2, Sec. 20 in Munkres' TOPOLOGY, 2nd ed: The dictionary order topology on $\mathbb{R} \times \mathbb{R}$ is metrizable.
80096
Prove that the union of countably many countable sets is countable.
67050
Every separable metric space has a countable base
145273
Disjoint $AC$ equivalent to $AC$
28819
A union of two subspaces not equal to the vector space.
81929
d-metrizable spaces are sequential
146664
The union of two linearly independent subsets
50880
Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
36315
Is $[0,1]$ a countable disjoint union of closed sets?
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
36184
Countability of disjoint intervals
41611
Open and closed set in n by n matrices space.
113534
Show that any metrizable space $X$ is Hausdorff