find a cochain map $ψ: A• → B•$ with a condition that $ψ^i:A^i→B^i$ is an inijective
73898
Give an example of cochain map which is bijective?
116732
Proving that a continuous map is surjective
44069
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
115999
Is there always an injective map from a space in its dual space?
14509
Contraction Map on Compact Normed Space has a Fixed Point
62711
Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism
86107
Map bounded if composition is bounded
42941
Pair of adjoint functors and showing that two certain maps are inverses
84437
Prove that the projection $p_i$ from the product space $X_I S_i \tau$ into $S_i \tau_i$ is open for each $i \in I$
100107
How can I prove that a linear map $T:V\to V$ such that $T^2 = I$ is equal to the Identity map?
153492
Let $p\colon X \to Y$ be a quotient map then if each set $p^{-1}({y})$ is connected, and if $Y$ is connected, then $X$ is connected.
107701
Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
72952
Uniqueness of a linear map on a basis of a vector space
98282
Prove that the function $\xi\in R \mapsto {e^{i\cdot \xi\cdot λ}-1\over i\cdot \xi}-λ$ is $C^{\infty}$
97801
If $R_{1}$ and $R_{2}$ are relations on a set S with $R_{1};R_{2}=R_{2};R_{1}$. Then $R_{1}$ and $R_{2}$ are bijective maps
94844
Unitary map between sets of vectors
111191
Show that $P_i$ and $\sum_i P_i$ being idempotent implies $P_i P_j=\delta_{ij}$