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Compactness
New post in Compactness
If every convergent subsequece converges to the same limit then the sequence converges
August 7th, 2020
sequences-and-series
compactness
metric-spaces
Topological counterexample: compact, Hausdorff, separable space which is not first-countable
August 1st, 2022
examples-counterexamples
first-countable
separable-spaces
general-topology
compactness
Is every compact space locally compact?
January 30th, 2020
compactness
general-topology
One point compactification of the rationals is not second countable
August 1st, 2022
general-topology
compactness
A subset of a metric space is closed iff its intersection with every compact subset is closed
August 1st, 2022
compactness
metric-spaces
general-topology
Compact spaces and closed sets (finite intersection property)
August 1st, 2022
compactness
general-topology
In a metric space, if a set is compact, then it is closed: improving proof
May 26th, 2020
compactness
metric-spaces
general-topology
real-analysis
Continuous, proper, injective map into first-countable space is homeomorphism onto image
August 1st, 2022
compactness
general-topology
Prove that the set of orthogonal matrices is compact
August 1st, 2022
orthogonal-matrices
real-analysis
general-topology
matrices
compactness
Hypothesis of Stone-Weierstrass Theorem
May 13th, 2020
metric-spaces
real-analysis
general-topology
functional-analysis
compactness
Limit point of an infinite set in a compact space
August 1st, 2022
general-topology
compactness
The two definitions of a compact set
August 9th, 2022
general-topology
real-analysis
compactness
Is one-point compactification of a space metrizable
August 1st, 2022
compactness
general-topology
second-countable
compactification
metric-spaces
Is $[ \sqrt 2, \sqrt 3] \cap \mathbb{Q}$ an open subset of $\mathbb{Q}$?
December 16th, 2020
general-topology
compactness
proof-verification
Topological properties of symmetric positive definite matrices
August 1st, 2022
connectedness
matrices
positive-definite
general-topology
compactness
Are one-point sets always compact in any topological spaces?
August 1st, 2022
compactness
general-topology
Difference between completeness and compactness
August 1st, 2022
complete-spaces
compactness
metric-spaces
general-topology
The set of traces of orthogonal matrices is compact
July 6th, 2020
general-topology
compactness
metric-spaces
orthogonal-matrices
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