Show that $T_\infty=\{U : X-U \text{ is infinite or empty or all of $X$} \}$ is a topology on $X$
31617
Is the collection $\tau_\infty = \{U:X-U$ is infinite or empty or all of $X\}$ a topology on $X$?
136158
$X$ has Indiscrete topology $\implies$ any subset of $X$ is connected
150796
Subspace topology and order topology (2)
47211
Does $\varphi(x)\le\int_0^x\varphi(t)dt$ for all $x\in[0,\infty)$ imply $\varphi\equiv0$.
123470
Why are box topology and product topology different on infinite products of topological spaces?
88205
How can I define a topology on the empty set?
100121
Assume that $(\text{X}, T)$ is compact and Hausdorff. Prove that a comparable but different topological space $(\text{X},T')$ is not.
17165
Is total boundedness a topological property?
3404
What are the convergent sequences in the cofinite topology
41690
Products of Continuous functions: Topology
81302
Showing that $a_n \in \ell^{\infty}$
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
88028
Topology - closures of intervals with the order topology
85285
Show $\sum_{i=1}^\infty x_i y_i$ is absolutely convergent
2575
Showing that $\mathbb{R}$ is connected
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
77563
Homeomorphism between spaces equipped with cofinite topologies