How do we prove the set of bounded and continuous functions between metric spaces is a complete subspace from the set of bounded functions?
74312
If Y is complete then B(X,Y) is complete
84264
the space of lipschitz function is complete with respect to some norm
12349
a construction of a continuous function from a normal space to [0,1]
53812
Metric is continuous function
87239
Prove functions defined by sup and inf are continuous
126944
Metric spaces problem
116069
Is every metric space a subspace of some connected metric space?
125682
Proof verification: the product of two continuous functions is continuous
144400
Are compact subsets of metric spaces closed and bounded?
61202
Show that $C[a,b]$ is a complete space under the metric $d(f,g)=\sup_{t\in [a,b]}|f(t)-g(t)|$.
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
54499
How do I show that all continuous periodic functions are bounded and uniform continuous?
94438
Show that the countable product of metric spaces is metrizable
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
95887
How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?
15480
Open set in a metric space is union of closed sets
118328
Metric space is totally bounded iff every sequence has Cauchy subsequence