Topology riddle - dense infinite subset
57868
Prove $\tau$ is cofinite on $X$ iff $(X,\tau)$ is $T_1$-space and any infinite subset of $X$ is dense in $(X, \tau)$
119624
A Dedekind infinite set has a countably infinite proper subset
95294
Dense subset of $C[0,1]$ which preserves rationals
66301
The cardinality of the set of countably infinite subsets of an infinite set
17544
another topology multiple choice
137621
The Number of Topologies on a Finite Set
144383
The closure of a connected set in a topological space is connected
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
59289
Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
14972
Cardinality of Vitali sets: countably or uncountably infinite?
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
107614
Partitioning an infinite set
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Every infinite set contains a countable subset
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
6523
Prove that the space has a countable dense subset
88595
Prob. 21, Sec. 17 in Munkres' TOPOLOGY, 2nd ed: Closure and complementation can result in at most 14 different sets
90590
Prove that the following set is dense