Is $\{(x,y)|y=\sin(\frac{1}{x})\}\cup(0,1)$ connected on $R^2$?
27581
Topologist's sine curve is connected
12104
How to prove this result involving the quotient maps and connectedness?
108808
$x =r\cos \theta$ and $y = r\sin\theta$, determine $\frac{\partial r}{\partial x}$ and $\frac{\partial \theta}{\partial x}$
97213
Why does $\sin(0)$ exist?
107076
Prove $S^1$ is not homeomorphic to $S^2$ using connectedness
43667
Is $f(x,y(x))$ a function of two variables? If so, how is that possible?
64993
Connectedness of the $S^2$ sphere
141643
Showing $\rho (x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric
117816
Is $\frac{x^2+x}{x+1}$ a polynomial?
23414
Topologist's Sine Curve: A rigorous proof of why $\overline{S} = S \cup V$
16517
Arcwise connected part of $\mathbb R^2$
149543
Prove that an annulus is not simply connected?
29970
Bounds of $I=\int_0^1\frac{\sin x}{\sqrt x}$ and $J=\int_0^1\frac{\cos x}{\sqrt x}$?
45319
Properties of $y$ if $\frac{d^2y}{dx^2}+xy=0$, $x \in [a,b],$ and $y(a)=y(b)=0.$
46642
Continuity of $\sin(x)/x$
97553
Continuity of $\frac{2xy}{x^2+y^2}$ at $(0,0)$
35754
Is $f(x)=\sin(x^2)$ periodic?