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$\bullet$ Linear Algebra

($1$) Corollary of Theorem 3, Section 2.2 of Hoffman’s Linear Algebra (link: https://math.stackexchange.com/q/4473121/861687)

($2$) Theorem 13, Section 3.4 of Hoffman’s Linear Algebra (link: https://math.stackexchange.com/q/4495476/861687)

($3$) Exercise 13, Section 3.4 of Hoffman’s Linear Algebra (link: https://math.stackexchange.com/q/4500574/861687)

($4$) Theorem 1, Section 5.2 of Hoffman’s Linear Algebra (link: https://math.stackexchange.com/q/4540412/861687)

($5$) Exercise 6, Section 5.2 of Hoffman’s Linear Algebra (link: https://math.stackexchange.com/q/4536877/861687)

($6$) Exercise 9, Section 5.3 of Hoffman’s Linear Algebra (link: https://math.stackexchange.com/q/4546362/861687)

($7$) Definition of Projection on $R$ along $N$ in Hoffman’s Linear Algebra (link: https://math.stackexchange.com/q/4626550/861687)

$\bullet$ Topology

($1$) Theorem 20.3 of Munkres’ Topology (link: https://math.stackexchange.com/q/4367787/861687)

($2$) Exercise 5, Section 20 of Munkres’ Topology (link: https://math.stackexchange.com/q/4373842/861687)

($3$) Exercise 6, Section 31 of Munkres’ Topology (link: https://math.stackexchange.com/q/4451175/861687)

($4$) Exercise 7(b), Section 31 of Munkres’ Topology (link: https://math.stackexchange.com/q/4452805/861687)

($5$) Exercise 1, Section 32 of Munkres’ Topology (link: https://math.stackexchange.com/q/4448298/861687)

($6$) Exercise 3, Section 32 of Munkres’ Topology (link: https://math.stackexchange.com/q/4460433/861687)

($7$) Exercise 1, Section 33 of Munkres’ Topology (link: https://math.stackexchange.com/q/4463970/861687)

($8$) Chapter 11, Theorem 5.2 (4) of James Dugundji Topology (link: https://math.stackexchange.com/q/4451556/861687)