The only proper subfield of $\mathbb C$ , which is path connected as a subset of $\mathbb C$ , must be $\mathbb R$?
71102
Subfields of $\mathbb{C}$ which are connected with induced topology
152442
An annulus in $\mathbb R^2$ is path connected
138911
Is $\mathbb R^2$ a field?
127365
Question on showing a bijection between $\pi_1(X,x_0)$ and $[S^1, X]$ when X is path connected.
155794
Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
55263
Path connected space that is not locally connected
14345
If $A\subset\mathbb{R^2}$ is countable, is $\mathbb{R^2}\setminus A$ path connected?
113216
No field properly between $\mathbb Q$ and $E$ iff $G(K/\mathbb Q) \cong A_4$ or $S_4$
4602
Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
57967
Difference between $\mathbb C$ and $\mathbb R^2$
88301
What are all of the connected subsets of $\mathbb{Q}$?
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
90816
Why does the product topology allow proper subsets for only finitely many elements?