Is the space of continuous bounded real valued functions on a Polish space separable?
123061
$X$ metric separable then $C(X)$ separable
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
121957
Is $p\mapsto \|f\|_p$ continuous?
67050
Every separable metric space has a countable base
71487
Real Analysis: Continuity of a Composition Function
30796
Is the set of irrationals separable as a subspace of the real line?
34173
Banach spaces and their unit sphere
17495
Show that the vector space of all continuous real-valued functions is infinite-dimensional
33114
Uniqueness of a continuous extension of a function into a Hausdorff space
50946
Separable Hilbert space have a countable orthonormal basis
75882
Countability of local maxima on continuous real-valued functions
46892
Inclusion of $L^p$ spaces
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
95074
Separability of $l^{p}$ spaces
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
8334
A reflexive Banach space is separable iff its dual is separable
25306
A countable family of point-wise bounded functions defined on finite measurable set is actually uniformly bounded on a closed subset