Show that $(0,1]$ is open in $[0,1]$ but $(0,1]$ is not open in $\mathbb{R}$
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
88155
Show that $[0, 1)\times[0, 1)$ is homeomorphic to $[0, 1]\times[0, 1)$ but not to $[0, 1]\times[0, 1]$.
16654
Unions and Intersections of Open Sets are Open
125962
The set $A'$ is closed in a $T_1$ space
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
17926
Zero divisor in $R[x]$
56728
Question about limit points of a Subset of $\mathbb{R}$
89125
Prove that $r \in R$ such that $0 \lt r \lt 1$ then $\frac{1}{r (1 - r)} \ge 4$
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
136106
Is every open subset of $ \mathbb{R} $ uncountable?
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
73130
A simple question about open set
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.
92774
Prove that a linear subspace of $C([0,1])$ is closed
50344
What is the closure of an open ball $B_X(\mathbf{a},r)$ in $X=\mathbb{R}^n$?