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Aout the quotient topology

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#general-topology #algebraic-topology
245
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Is Converse True, i.e Quotient space of any space is locally connected then space is locally connected?

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#general-topology #connectedness #quotient-spaces
542
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Proving $\mathscr{B}$ is a basis of the Sorgenfrey line

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#real-analysis #general-topology #proof-writing
573
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$v-e+f=2-2g$ as a topological invariant

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#general-topology #polyhedra
587
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Proving Sorgenfrey line not homeomorfpic to $\mathbb{R}$ and $\mathbb{R}^2$ and its subspaces

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#real-analysis #general-topology #proof-writing
97
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Which is the difference between these two sets?

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#general-topology #notation #manifolds #mathematical-physics
320
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Is every totally disconnected topological group locally profinite?

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#general-topology #topological-groups #profinite-groups
236
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Prove that if $x^1,\dots,x^m$ are linearly independent then $C = \text{cone}(\{x^1,\dots,x^m\})$ is closed.

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#real-analysis #general-topology #vector-spaces #convex-analysis
169
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What are the subsets of $\{\{n\alpha\} \:|\: n\in\mathbb{N}\}$ which are dense in $[0,1)$?

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#general-topology #number-theory
263
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Every group of totally disconnected type is locally profinite?

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#general-topology #topological-groups #profinite-groups
150
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The family of all subsets of $X$ that contain a fixed set $Q$ is regular under what conditions?

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#general-topology #separation-axioms
76
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How to deduce Jordan Curve Theorem from Schönflies Theorem

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#general-topology #curves #geometric-topology #plane-curves
99
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Removing a closed subset from a surface gives a surface

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#general-topology #surfaces #geometric-topology
123
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Can a convergent net over a countable set have a subsequence?

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#general-topology #functional-analysis #order-theory
1k
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CW-complex structure on the quotient

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#general-topology #algebraic-topology #quotient-spaces #cw-complexes

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