Example 1313 Consider the space C(K) of continuous functions f K !R on a compact set KˆR with the supnorm metric de ned in Example 139 The ball B r(f) consists of all continuous functions g K!R whose values are within rof the values of f at every x2K For example, for the function f shown in Figure 1 with r= 01, the open ball BV i si t H UD N e w J e r se y f o r Mo r e I n f o r m a t i o n Su bsc r i be t o t h e H UD Re gi o n I I N e wsl e t t e rL G A P R D K O W I T Z K R D LACOMB RD C O R N E L I U S P A S S R D A I R I E R D V A L S E T Z R D P E R Y D A L E R D C A S C A E H W Y P O O D L E C R R D DEC ER RD B E L L F O U N T A I N R D DAWSON RD L eg nd Cities ODFW Headquarters ODFW Regional Offices Highways Major Roads Trails Pow erlin s Cou nty Li e Wat er Bodi s Major Streams
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