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 8h asked Flip/flop of finite joins and finite meets of lattices Apr 23 comment Product of directed partial orders I've also asked it at sci.math: groups.google.com/forum/#!topic/sci.math/leERWkEI91I Apr 23 comment Product of directed partial orders In one direction it is easy: Suppose one multiplier is not a dcpo. Take a chain with fixed elements (thanks our posets are nonempty) from other multipliers and for this multiplier take the values which form a chain without the join. This proves that the product is not a dcpo. Apr 23 revised Product of directed partial orders added 22 characters in body Apr 23 asked Product of directed partial orders Apr 18 comment Explicit formulas for meets and joins of uniform spaces From the previous comment it follows that sets of uniform spaces (and proximity spaces too) always have a join. So they are complete lattices. I am trying to write down the formulas for meets Apr 18 comment Explicit formulas for meets and joins of uniform spaces OK, I see that join of uniform spaces is just join of filters (and it is similarly understood by me about join of proximities). The remaining question is about meets of uniform spaces and proximity spaces Apr 18 revised Explicit formulas for meets and joins of uniform spaces added 151 characters in body Apr 18 asked Explicit formulas for meets and joins of uniform spaces Apr 17 revised Is there another notation for this set-theoretic formula? edited body Apr 17 comment Is there another notation for this set-theoretic formula? It seems you've misunderstood me. I do not ask for another symbol with the same meaning as $\prod$. Instead I ask for another (but equal for all $S$) way to describe an expression, that is an equal expression which has a different structure. Apr 17 revised Is there another notation for this set-theoretic formula? that I write a book Apr 17 comment Is there another notation for this set-theoretic formula? @Stefan I am writing a book. If during writing I notice that some formula can be rewritten in another way, I should add the alternative notation to my manuscript. This is why I look for another notation. The desired properties are only two: 1. be different; 2. be simple enough Apr 17 comment Is there another notation for this set-theoretic formula? @Stefan It seems that you haven't noticed that I have the words "other" in my question. I ask for another way Apr 17 comment Is there another notation for this set-theoretic formula? @Stefan I am searching for a wide-spread alternative notation which is "simple" (that is is a short formula) Apr 17 comment Is there another notation for this set-theoretic formula? No $\prod_{X\in S} X$ is not the same as $X$. It is selection of one element from every $X$. Apr 17 comment Is there another notation for this set-theoretic formula? Why have you decided that "we" want "that"? I want $\operatorname{im} P$ and this is not disputed :-) Apr 17 asked Is there another notation for this set-theoretic formula? Apr 13 comment Is there a term in lattice theory for this? The best term I've come up is "quasi upward directed set". But it's entirely nonstandard (and also too long, as consists of four words). Apr 13 asked Is there a term in lattice theory for this?