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May
12
answered Let $(X, \mathfrak T)$ be a topological space and suppose that $A$ is a subset of $X$. Then 1. $Cl(A) = Cl(Int(A))$ 2. $Int(A) = Int(Cl(A))$
May
12
answered Sum of open/closed/compact sets in $\mathbb{R}^n$ open/closed/compact
May
11
answered $[0,1]\times\mathbb{N}/(0,k)$ not metrizable.
May
11
answered injective/path component
May
10
answered Equivalence of sequence spaces
May
10
answered Path components
May
7
answered Why is the set of integers in $\mathbb{R}$ closed?
May
7
answered Can Fatou's lemma and monotone convergence theorem be considered as equivalent?
May
7
answered Example 3, Sec. 25 in Munkres' TOPOLOGY, 2nd ed: Why is the topologist's sine curve not locally connected?
Apr
9
answered Why does closedness and boundedness for $S = \{ v \in V : || v||_{\infty} = 1\}$ imply that $S$ is compact in a finite dimensional vector space $V$?
Mar
27
answered Why the column space of a matrix is useful?
Mar
27
answered Integrals of indicator functions question
Mar
26
answered Let $X$ be a topological space. Prove that for any $x $ in the intersection of all opens sets $=\{x \}$, the space $X$ need not be Hausdorff.
Mar
26
answered Prove $f$ is diagonalizable iff $V=W \oplus Z$ where $W,Z \subseteq V$ are $f$ invariant
Mar
24
answered Are $l^p$ spaces compact?
Mar
24
answered infinite Union of compact sets
Mar
19
answered Compact Projections to $S^1$
Mar
12
answered Countability of certain subset of $\mathbb{R}$
Mar
12
answered what can you conclude about the number of solutions of the linear system Ax = b?
Mar
10
answered A doubt in Probability essentials by Protter