please answer only #3 asap all information provided

standing Notation and basic conventions. Throughout let X and Y denote topological spaces, and for a subset A of a topological space denote its closure by A. 1. State precise technical definitions of four of the following . continuous, . closure, . limit point, . compact, and . product topology (on a not necessarily countable product of topological spaces). 2. Prove ONE of the following two (you will earn credit for only one). . Every closed subset of every compact space is compact. . The continuous image of every path connected space is path connected. 3. In which of the product, uniform, and box topologies do the sequences (a,). (b,), C RW converge? Justify your answers. = (1, 1, 1, 1, 1, 1, 1, . .. ) 11 = (1, 1, 2, 4, 8, 16. 32. ...) = (1, BELL 43 = (1, 1, 1, 3, 9, 27, 81, ...) b3 = (1, = (1, 1, 1, 1, 4, 16, 64. ... ba = (1 = nmax(0,4-m) brak