313-15-Final - VUW NANGA O TE U POKO O TE IKA A MA UI TE WHARE WA VICTORIA UNIVERSITY OF WELLINGTON EXAMINATIONS 2015 TRIMESTER 1 MATH 313 TOPOLOGY Time

# 313-15-Final - VUW NANGA O TE U POKO O TE IKA A MA UI TE...

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T E W H A R E W ¯ A N A N G A O T E ¯ U P O K O O T E I K A A M ¯ A U I VICTORIA U N I V E R S I T Y O F W E L L I N G T O N EXAMINATIONS – 2015 TRIMESTER 1 MATH 313 TOPOLOGY Time Allowed: THREE HOURS CLOSED BOOK Permitted materials: No calculators permitted Instructions: Answer all six questions. All questions are of equal value. Begin each main question (1, . . . , 6) on a new page. MATH 313 Page 1 of 3
1. Let A be a subset of a topological space. (a) Define the i nterior, closure, boundary and exterior of A . State a characterisation of the closure points of A . (b) Let x be interior to A . Show that x is exterior to X - A . (c) In the standard topology on R , what is the boundary of the set Q of rational num- bers? Give a full proof of your answer. 2. (a) Let f : X Y be a continuous function between topological spaces. Define the notion of f being continuous at a point x of X . Give a proof that f is continuous at every point of X .

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• Summer '19
• Math, Topology, Homeomorphic, Topological space, Three hours, topological spaces, University of Wellington

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