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Is the classifying space $B^nG$ the Eilenberg-MacLane space $K(G, n)$?

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#algebraic-topology #homotopy-theory #classifying-spaces #eilenberg-maclane-spaces
58
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f,g: X $\rightarrow $Y homeomorphisms that are homotopic. Then $f^{-1}$ and $g^{-1}$ are homotopic.

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#general-topology #homotopy-theory
148
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Proof category of $k$-spaces is "almost" locally Cartesian closed

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#general-topology #algebraic-topology #category-theory #homotopy-theory
342
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When does pullback along a continuous map admit a left adjoint?

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#general-topology #algebraic-topology #category-theory #homotopy-theory #adjoint-functors
132
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The induced homomorphisms of maps homotopic relative to a subset are the same

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#algebraic-topology #homotopy-theory
1.2k
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Proving a homotopy is continuous

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#algebraic-topology #continuity #homotopy-theory
1k
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If the map induces identity on all homotopic groups then it is homotopic to identity

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#algebraic-topology #homotopy-theory #geometric-topology
98
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What does Allen Hatcher mean by "tack $F$ onto $f$"?

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#algebraic-topology #homotopy-theory
204
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If $f$ and $g$ are homotopic from $X$ to $Y$ and $p : W \rightarrow X, q: Y \rightarrow Z$, then...

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#algebraic-topology #proof-explanation #homotopy-theory
98
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Bijection of pair of top spaces

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#general-topology #algebraic-topology #differential-topology #homotopy-theory #topological-vector-spaces
428
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Change general path homotopy to path homotopy relative to endpoints

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#general-topology #homotopy-theory #fundamental-groups
431
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The sphere is simply connected using a cover of two hemispheres.

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#algebraic-topology #homotopy-theory #fundamental-groups
259
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Question about definition of differentiable homotopy

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#real-analysis #derivatives #homotopy-theory
89
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Bijection between triple of spaces.

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#general-topology #algebraic-topology #homotopy-theory #topological-groups
372
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Retract of a torus.

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#algebraic-topology #homotopy-theory

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