Let $(X,\mathscr U)$ be a uniform space. Then why does $\mathcal N_x=\{U[x]\ |\ U\in\mathscr U\}$ form a neighborhood base for $x\in X$?
121889
Neighbourhood filter of a uniform space
145222
The dual of subspace of a normed space is a quotient of dual: $X' / U^\perp \cong U'$
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
98762
$f_n(x) = x - x^n$ for $x\in [0,1]$. Does the sequence converge pointwise or uniformly on $[0,1]$?
7723
Countable basis of function spaces
65494
Proper subspaces of $ R^n $
147914
Closed image of locally compact space
101506
Why is $1, (x-5)^2, (x-5)^3$ a basis of $U=\{p \in \mathcal P_3(\mathbb R) \mid p'(5)=0\}$?
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
130361
Basis for a topology with a countable number of sets
35547
Does $\{f_ng_n\}\to fg$ uniformly?
102048
Closure of a compact set in Regular space $ X $
114437
Why is this the basis for the indiscrete topology?
138653
Is $\mathbb{R}$ a subspace of $\mathbb{R}^2$?
41482
$f_n → f$ uniformly on $S$ and each $f_n$ is cont on $S$. Let $(x_n)$ be a sequence of points in $S$ converging to $x \in S$. Then $f_n(x_n) → f(x)$.
33207
Bases having countable subfamilies which are bases in second countable space
119804
If $\lim_{n\to \infty}a_n = a\in \mathbb{R}$ . Prove that $\limsup_{n\to \infty}a_n x_n=a\limsup_{n\to \infty}x_n$ .