Closed Linear spaces and the direct sum
35625
Direct sum of orthogonal subspaces
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
18023
The direct sum $\oplus$ versus the cartesian product $\times$
147961
Characterizing simply connected spaces
92774
Prove that a linear subspace of $C([0,1])$ is closed
89264
Connectedness in the Quotient Space
64484
Left ideal $I$ is a direct summand of $R$ iff $I = Rr$, $r^2 = r$
82355
When is the image of a linear operator (between Banach spaces) closed?
69893
An inner product space and its proper closed subspace with trivial orthogonal complement
16512
Product of $T_1$ spaces is $T_1$
4319
Vector space can be written as direct sum of subspaces
11586
Sequences of Real Numbers in a closed bounded interval
127575
Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
35855
Closed form for an infinite product
140225
Linear transformation maps the first quadrant to a closed set
95887
How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?
121047
Proof: Sum of dimension of orthogonal complement and vector subspace