Continuous function, mapping of a set to itself
7358
For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous.
4538
Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous?
147788
Why is every map to an indiscrete space continuous?
29582
Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
132478
Prove that continuous functions mapping irrationals to rationals must be constant
20284
Continuous injective map is strictly monotonic
116732
Proving that a continuous map is surjective
153495
Continuous function does not map closed set to closed set
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
26687
Show that $f$ maps the unit circle to itself
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
64619
Continuity of a function of product spaces
32359
Inner product of two continuous maps is continuous
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition