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Second countability from a continuous open map

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#general-topology #second-countable
131
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For what definition of local compactness are locally compact and second-countable spaces $\sigma$-compact?

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#general-topology #compactness #second-countable
405
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A second countable space is countably compact iff it is compact

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#general-topology #compactness #second-countable
18
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Has the topology of inferior semicontinuity a countable base?

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#sequences-and-series #general-topology #elementary-set-theory #second-countable
731
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Topological properties of Sorgenfrey line.

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#general-topology #compactness #connectedness #second-countable #first-countable
202
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Why is this space not second-countable?

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#general-topology #second-countable
316
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First countable, second countable, and Lindelöf

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#general-topology #second-countable #first-countable #lindelof-spaces
314
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Why is the topology on the Sorgenfrey line not second countable?

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#general-topology #second-countable #sorgenfrey-line
128
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Second Countability Implies Separability

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#general-topology #proof-explanation #separable-spaces #second-countable
201
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On showing that every separable metric space has a countable base

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#real-analysis #general-topology #metric-spaces #separable-spaces #second-countable
145
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Does second countablity implies closed (or open) set in $X$ is a countable intersection of open sets in $X$?

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#general-topology #second-countable
57
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Why the the new basis is countable?

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#general-topology #elementary-set-theory #proof-explanation #second-countable
180
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Example of a Hausdorff topology that is homeomorphic to $\mathbb R^n$ but isn't second countable?

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#general-topology #differential-geometry #manifolds #examples-counterexamples #second-countable
220
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Does every Lie group have at most countably many connectected components?

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#general-topology #differential-geometry #lie-groups #connectedness #second-countable
1.1k
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How to tell if a space is second-countable

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#general-topology #hilbert-spaces #intuition #second-countable

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