Set up varnish, but is the content really from cache?

Let $D=\{0\}$ be the one-point discrete space. Let $f:\mathbb{R}\to\mathbb{R}:x\mapsto x$ be the identity map, and let $g:\mathbb{R}\to D:x\mapsto 0$. Both $f$ and $g$ are easily seen to be closed, but $f\times g:\mathbb{R}^2\to\mathbb{R}\times D$ is not: it maps the graph of $xy=1$, which is a closed set in $\mathbb{R}^2$, to $$\Big(\mathbb{R}\setminus\{0\}\Big)\times\{0\}\;,$$ which is not closed in $\mathbb{R}\times D$: $\langle 0,0\rangle$ is in its closure.

You are experiencing the difference between "system naming convention" and "SQL naming convention" modes. Originally, system naming mode required a slash character / as the delimiter when qualifying with a schema name, while SQL naming mode used a period . delimiter. An update to v7.1 now allows either delimiter when using system naming. V5R3 is no longer supported, nor updated. On a green screen session you can specify STRSQL NAMING(*SYS). Or specify system naming convention on your JDBC/ODBC connection string settings.

There are other functional differences between the two modes. See here and here. Chief among them is that system naming mode allows use of the library list, as long as you don't specify a CURRENT SCHEMA. But you can specify a current library, with the CHGCURLIB command in CL, or in SQL with CALL QCMDEXC('CHGCURLIB MYLIB',15) (where 15 is the length of this sample command)

DB2 for i catalog views may be found in QSYS2.

SELECT COLNO
      ,SYSTEM_COLUMN_NAME   
      ,DATA_TYPE 
      ,coalesce(PRECISION,LENGTH)        as len
      ,smallint(SCALE)                   as dp
      ,STORAGE                           as bytes
      ,varchar(COLUMN_TEXT,50)           as fldtext  
      ,varchar(substr(LABEL, 1,20),20)   as hdg1
      ,varchar(substr(LABEL,21,20),20)   as hdg2
      ,varchar(substr(LABEL,41,20),20)   as hdg2
      ,CCSID
      ,IS_NULLABLE
FROM QSYS2/SYSCOLUMNS
WHERE SYSTEM_TABLE_SCHEMA = 'MYLIB' 
  AND SYSTEM_TABLE_NAME   = 'SOMEPF'

Most IBM i shops used 10-character names (operating system rules) and typically did not use 128-character names allowed by DB2, so generally SYSTEM_COLUMN_NAME, SYSTEM_TABLE_NAME, and SYSTEM_SCHEMA_NAME will be sufficient.

The V5R3 SQL Reference is available as a PDF, as Dave Jones mentioned.

Perhaps of some interest it might be the following example showing that the product of identical closed maps need not to be closed. Let $f\colon\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=\max\{0,x\}$. Then $f$ is closed since $f[A]$ is either $A$ or $(A\cap[0,\infty))\cup\{0\}$. But $f\times f$ is not, as it maps $\{(x,y)\!:x\cdot y=-1\}$ to $(\{0\}\times(0,\infty))\cup((0,\infty)\times\{0\})$.