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Properties of the boundary of a set

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#general-topology
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$f: C_*\to D_*$ is a homotopy equivalence between chain complexes. Prove that $f_*: H_n(C_*)\to H_n(D_*)$ is an isomorphism

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#abstract-algebra #general-topology #algebraic-topology #homological-algebra
119
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Passing from a diagonal to a covering uniformity and vice versa

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#general-topology #uniform-spaces
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Show that the Euler characteristic of a chain complex is equal to the Euler characteristic of its homology

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#abstract-algebra #general-topology #algebraic-topology #homological-algebra #homotopy-theory
80
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Continuous function from complex matrices to complex numbers

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#general-topology #matrices #connectedness
240
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The set of all probability measures on $(\Xi,\mathcal{B})$ is weakly compact with respect to topology of total variation?

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#general-topology #probability-theory #measure-theory #convergence-divergence
42
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A Question About Homeomorphisms And Geography

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#general-topology
223
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Totally bounded space.

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#general-topology #functional-analysis #metric-spaces #compactness
448
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Finite intersection property for a subset

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#real-analysis #general-topology #functional-analysis
305
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Proving connectedness of a topological group using identity component

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#general-topology #group-theory #metric-spaces #connectedness #topological-groups
40
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Existence of a sequence which realizes an element from a closure

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#real-analysis #general-topology
91
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Countable union of open sets

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#calculus #real-analysis #general-topology
1k
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Prove that $C_*$ is acyclic if and only if the trivial homomorphism $f_*: C_*\to D_*$ is a homotopic equivalence.

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#abstract-algebra #general-topology #algebraic-topology #homological-algebra #homotopy-theory
440
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What is the derived set ( D(A) = ? ) in this example?

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#general-topology
647
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Reference for CW-Complexes

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#general-topology #reference-request #algebraic-topology #book-recommendation #cw-complexes

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