id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-1907	Amalraj. P	Stability, and Almost Sensitivity of Induced Maps	2024	8	.pdf	application/pdf	3283	213	84	We prove that there exist a sequence {𝑓�̃�} in 𝜓(𝐶(𝑋))which converges to F such that there is f ∈ C(X) satisfies 𝑓 = 𝐹. Consider 𝜓−1(𝑓𝑛) = 𝑓𝑛. For every ϵ > 0, take N > 0 such that 𝑑(𝑓𝑛, 𝑓𝑚) < ϵ, for every n,m ⩾ N and all x ∈ X. Since {fn} is a cauchy in C(X), which is a complete metric space, there exist f ∈ C(X) such that {fn} converges to f. Since 𝜓 is continuous {𝜓(𝑓𝑛)}	cache/cana-1907.pdf	txt/cana-1907.txt