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Punctured open set is not contractible

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#general-topology #algebraic-topology #homotopy-theory
187
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Definition of homotopy fiber

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#algebraic-topology #homotopy-theory #model-categories
683
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What can we say about two topological spaces with the same fundamental group?

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#general-topology #algebraic-topology #homotopy-theory #fundamental-groups
129
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Homotopy invariance of pullbacks of principal bundles

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#algebraic-topology #homotopy-theory #principal-bundles #classifying-spaces
104
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If all continuous maps from $S^1 \to X$ are homotopic, then all paths from $x_0$ to $x_0$ are homotopic.

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#algebraic-topology
105
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Proof of $\pi_1(S^n)=0$ if $n \geq 2$.

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#algebraic-topology #homotopy-theory
639
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Homology - long exact sequence from short exact sequences of cofibrations

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#algebraic-topology #homological-algebra
41
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Fundametal group and continuous extension to $\Bbb R^n$

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#algebraic-topology #fundamental-groups
575
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Open Sets in the Wedge Sum and a Homeomorphism

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#algebraic-topology #quotient-spaces
516
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Find finite path connected topological space with $π_1 (X, x_0 ) \cong \Bbb Z/2\Bbb Z$

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#general-topology #algebraic-topology #fundamental-groups
245
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Bing's house, but with n rooms?

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#algebraic-topology
575
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homotopy equivalence between the cylinder of a map

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#algebraic-topology #homotopy-theory
260
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Mod p cohomology operations and homotopy groups of spheres

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#algebraic-topology #stable-homotopy-theory
131
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existence of space and deformation retraction

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#algebraic-topology
636
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A map that has no lift

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#general-topology #algebraic-topology

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