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Theorem 4.28 reads as follows:View attachment 3855In the proof of the above theorem, Apostol writes:

" ... ... Let \(\displaystyle m = \text{ inf } f(X)\). Then \(\displaystyle m\) is adherent to \(\displaystyle f(X)\) ... ... "

Can someone please explain to me exactly why \(\displaystyle m = \text{ inf } f(X)\) implies that \(\displaystyle m\) is adherent to \(\displaystyle f(X)\)?

Help will be appreciated ... ...NOTE: In the above proof Apostol makes mention of an adherent point, so I am providing Apostol's definition of an adherent point together with (for good measure) his definition of an accumulation point ... ...View attachment 3856