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Sharkovsky's Theorem and Triangular Functions

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#general-topology #dynamical-systems #periodic-functions
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Is it true that every totally bounded set in a metric space is compact?

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#real-analysis #general-topology #metric-spaces
155
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Graph of the composition of a continuous function and a correspondence with a graph homeomorphic to its domain

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#general-topology #continuity #set-valued-analysis
68
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If $A\subset B$ and $B=V_1\cup V_2$, where $V_1$ and $V_2$ are open sets, why are the sets $A\cap V_1$ and $A\cap V_2$ open?

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#general-topology
1.2k
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Proof of Arzela's Theorem

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#real-analysis #general-topology #arzela-ascoli
202
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(Co)homology of $S^2×S^2/ℤ_2$

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#general-topology #algebraic-topology
763
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A sequence of rationals converging to an irrational point (proving that $\mathbb Q$ is not locally compact)

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#sequences-and-series #general-topology #compactness
484
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Hatcher Lemma 1A.3 - Covering Spaces Of Graphs Are Graphs

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#general-topology #algebraic-topology
45
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Is this argument about sequential compactness wrong?

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#general-topology
136
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The smallest compactification for continuous extension of $\sin(x)$

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#general-topology
146
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find a free ultrafilter on $\Bbb N$

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#general-topology #convergence-divergence #filters
135
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Frontier properties of a subset of $\mathbb{R}$

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#general-topology
93
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Topology of decomposition of a space

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#general-topology #algebraic-topology #vector-bundles
154
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cluster and convergence points

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#real-analysis #general-topology #logic
253
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Generalization of topologies with equivalence classes of sets

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#general-topology #functional-analysis #reference-request #equivalence-relations

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