Let A and B be countable sets. Is there any function f such that a certain condition holds for an uncountable number of functions g?
63678
Let $A$ and $B$ be countable sets. Is there any function $f$ such that a certain condition holds for an uncountable number of functions $g$?
40937
Is the set of partial order relations over $ \mathbb{N}$ countable?
157821
Let $S$ be a finite set. Show that any function $f: S \rightarrow \mathbb{R}^n$ is continuous on S. What if $S$ is countably infinite?
145428
Set $A$ is countably infinite if and only if there exists a bijection $f: \mathbb{N} \rightarrow A$
57021
Is the set of all functions $f:Z_+\rightarrow Z_+$ that are eventually constant countable.
132868
Bijection between an infinite set and its union of a countably infinite set
104842
Let $X$ be uncountable. Then the set of injective functions $f\colon X \to \mathbb{R}$ has empty interior in $\mathscr{C}(X;\mathbb{R})$
68230
The cardinality of a countable union of sets with less than continuum cardinality
99599
Uncountable and countable
91237
Every infinite set contains a countable subset
117133
Is there an infinite countable $\sigma$-algebra on an uncountable set
58471
Accumulation points of uncountable sets
9021
An infinite subset of a countable set is countable
48765
Let $S$ and $T$ be finite non-empty sets such that $|S| = |T|$. Show that the function $f : S\to T$ is onto if and only if it is one-to-one.
155168
Is the collection of finite subsets of $\mathbb{Z}$ countable?
154474
Image of countable and uncountable sets
68994
Countable closed sets