A concern on the definition of compactness in a metric space
7871
Are "if" and "iff" interchangeable in definitions?
108619
Proving Baire's theorem: The intersection of a sequence of dense open subsets of a complete metric space is nonempty
133152
(X,d) be a compact metric space. For every open cover, show there exists ε > 0 such that ∀𝑥 ∈ X, B(x,ε) is contained in some member of the cover.
74607
Variation of the metric with respect to the metric
39076
Contraction of compact sets
126759
Unbounded continuous function on non-compact metric space
99645
Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
94672
Why is the triangle inequality property important for metric spaces?
36566
Equivalence classes and metric spaces
98609
Does pointwise equicontinuous and uniformly equicontinuous implies compactness?
50677
Is this metric space incomplete?
49374
Closure of a subset in a metric space
121135
Why don't we use closed covers to define compactness of metric space?
42638
Showing that a function $f$ has a unique fixed point in a metric space.
35652
Every compact metric space is complete
69528
Metrizability of quotient spaces of metric spaces
25752
What should be the intuition when working with compactness?