How to construct a continuous function from a non compact metric space to R that is unbounded?
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
1014
Pointwise limit of continuous functions not Riemann integrable
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
153495
Continuous function does not map closed set to closed set
120947
continuous real-valued function
95831
Compactness and sequential compactness in metric spaces
144353
A closed ball in a metric space is closed
70106
diameter on a compact metric space
36149
A uniformly continuous function maps bounded set to bounded sets
35156
Constructing a choice function in a complete & separable metric space
137881
A not complete metric space?
147287
Is it possible to construct a metric in $\mathbb{R}^n $ s.t. it does not induce CONVEX balls?
17607
Open maps which are not continuous
55679
Does there exist a continuous function from [0,1] to R that has uncountably many local maxima?
148931
Constructing a function that is continuous and has a max on an open interval, but is not necessarily increasing immediately to the left of the max.
108997
Continuous functions that attain local extrema at every point