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Articles: 35
A metric space is a set equipped with a nonnegative symmetric distance satisfying definiteness and the triangle inequality.
Table of contents
1k
35
Convergence in a metric space
Metric space
24
Sequential characterization of continuity in metric spaces
Metric space
46
Sequential compactness of a compact metric space
Metric space
21
Normality of every metric space
Metric space
39
Bounded-continuous-function characterization of compact metric spaces
Metric space
46
Completeness
Metric space
14
Triangle inequality
Metric space
14
Euclidean distance
Metric space
8
Diameter of a metric space
Metric space
13
Uniform continuity
Metric space
67
2
Heine-Cantor theorem
Uniform continuity
15
Uniform limit theorem for uniformly continuous functions
Uniform continuity
33
Equivalent metrics
Metric space
96
2
Equivalent metrics need not be bi-Lipschitz equivalent
Equivalent metrics
31
Equivalent codomain metrics need not preserve uniform convergence
Equivalent metrics
41
Distance to a set
Metric space
17
Isolated point
Metric space
29
Complete metric space
Metric space
873
14
Cantor intersection theorem
Complete metric space
33
Baire category theorem
Complete metric space
608
7
Closed convex absorbing set has an origin neighbourhood
Baire category theorem
115
1
Closed symmetric absorbing set without an origin neighbourhood
Closed convex absorbing set has an origin neighbourhood
61
Isolated points in a countable complete metric space
Baire category theorem
85
Nowhere dense set
Baire category theorem
32
Meagre set
Baire category theorem
11
Generic nowhere-monotone continuous function
Baire category theorem
72
Smooth function with a pointwise vanishing derivative
Baire category theorem
209
Space of smooth functions on a compact interval
Complete metric space
187
3
Completeness of the smooth-function metric
Space of smooth functions on a compact interval
41
Generic superfactorial derivative growth at rational points
Space of smooth functions on a compact interval
123
1
Nowhere-analytic generic smooth function
Generic superfactorial derivative growth at rational points
53
Closed-subspace completeness theorem
Complete metric space
29
Hausdorff distance
Metric space
101
2
Closed singleton embedding in a Hausdorff hyperspace
Hausdorff distance
62
1
Completeness is reflected by the Hausdorff hyperspace
Closed singleton embedding in a Hausdorff hyperspace
30
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Topological analysis
Analysis
Area of mathematics
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