How to show that $\mathbb{N}$ is a Baire space
140472
Is the space $\mathbb{N}$ is a baire spaces ? yes/No
46563
Show that the quotient space is homeomorphic to the n-disc
14215
Show that the union $\bigcup A_n$ has empty interior in $X$
102485
Showing that a topological space is ${\rm T}_1$
2575
Showing that $\mathbb{R}$ is connected
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
154076
How to show this property of $\mathbb{RP}^{n}$.
145926
To show that $\sum a_nb_n$ is absolutely convergent
53261
Show that Pn is an (n+1)-dimensional subspace
27400
About Baire's Category Theorem(BCT)
116768
Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?
139078
Infinite partition of $\mathbb N$ by infinite subsets
7678
Show "countable complement topology" is a topology
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
83116
Uncountability of basis of $\mathbb R^{\mathbb N}$
132653
How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?