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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?
Apr
7
comment Generalizing a theorem about filters on a boolean lattice
Maybe, it holds for all Heyting or all co-Heyting lattices?