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Topological properties of Sorgenfrey line.

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#general-topology #compactness #connectedness #second-countable #first-countable
316
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First countable, second countable, and Lindelöf

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#general-topology #second-countable #first-countable #lindelof-spaces
60
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Axioms of countability

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#general-topology #first-countable
75
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Is this a non-first-countable space?

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#general-topology #first-countable
100
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Directly proof $S$ is countable, where $S$ is set of function from $\{0, 1\}$ to $\mathbb{N}$

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#elementary-number-theory #elementary-set-theory #natural-numbers #elementary-functions #first-countable
69
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First countable space and convergent sequences

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#general-topology #first-countable
46
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Why is the ordered square $[0,1]^{2}$ first countable in the dictionary order?

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#general-topology #first-countable
54
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Recasting Algorithmic Information In Terms of Finite Directed _Cyclic_ Graphs?

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#combinatorics #number-theory #discrete-mathematics #graph-theory #first-countable
153
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Countable basis and first countable

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#general-topology #first-countable
77
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Topology counterexamples without ordinals

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#sequences-and-series #general-topology #compactness #second-countable #first-countable
113
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Countable Complement Space is not First-Countable

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#general-topology #first-countable
224
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$\prod_{n=1}^{\infty}{\mathbb{R}}$ endowed with the box topology is not first countable.

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#sequences-and-series #general-topology #convergence-divergence #first-countable #box-topology
86
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Lower semicontinuity of parameter dependent Lebesgue integral

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#measure-theory #lebesgue-integral #first-countable
87
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Definition of Countability in Munkres’ Topology

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#general-topology #definition #second-countable #first-countable
92
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Exercise 1(a), Section 30 of Munkres’ Topology

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#general-topology #solution-verification #proof-writing #alternative-proof #first-countable

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