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An amateur general topology researcher.


Jul
19
comment Filters on a set of filters, are they equivalent to just filters?
@PatrickDaSilva $U$ is a set. It does not "have poset structure".
Jun
22
comment Help to conceive a name
Or even "mixer" as an opposite for "filter"
Jun
22
comment A term for category where every loop of morphisms is an identity
An additional property of my particular category, is that there exist isomorphisms between every two objects. Is there a term for this?
Jun
22
comment A term for category where every loop of morphisms is an identity
@AndreasBlass: Sorry, but WHAT can really happen?
Jun
22
comment A term for category where every loop of morphisms is an identity
@MaliceVidrine: I am totally ignorant in topoi theory, and so can't value the beautify of your comment
Jun
22
comment A term for category where every loop of morphisms is an identity
OK, the object I am thinking about is a thin category. (Moreover it is a thin groupoid.) My question is satisfied now.
Jun
22
comment Help to conceive a name
Hm, maybe I will stop at naming it "selector". This word is pretty much similar to the word "filter" in its informal meaning
Jun
22
comment Defining principal elements of every poset. Is this a new idea?
"So in a lattice every element except $0$ is principal." It is wrong: non-principal filters are non-principal in this sense. It seems you confuse for-all-filters with for-all-principal-filters or for-all-ultrafilters. I haven't check the details, but I am sure in the lattice of filters on a set, not only $0$ is principal
Jun
22
comment Help to conceive a name
Or maybe name it "restraint"?
Jun
22
comment Help to conceive a name
Or maybe name it "confinement"? (but now I like "restriction" more)
Jun
22
comment Help to conceive a name
May I name it "restriction"?
Jun
22
comment What are the names for the structures obtained when we drop some topological space axioms?
So, you are interested in structures, more general than topologies. If you "drop" (and add instead other weaker axioms) the requirement that elements of a topology are sets, you get locales and frames: en.wikipedia.org/wiki/Pointless_topology And an other generalization (however not similar at all to just dropping some axioms) of topologies is my research of "funcoids": mathematics21.org/algebraic-general-topology.html
Jun
22
comment Help to conceive a name
A special case of a set conforming to the fourth formula is $F = \{A\in\mathscr{P}U \,|\, A\nsupseteq P\}$ for a set $U$ and its subset $P$.
Jun
21
comment Defining principal elements of every poset. Is this a new idea?
@OlivierBégassat: See "Moreover, my idea can be generalized from complete lattices to arbitrary posets..." near the bottom of my question
Jun
21
comment Defining principal elements of every poset. Is this a new idea?
@OlivierBégassat: Yes, but only for lattices with a bottom element, not for arbitrary posets. My definition is valid for any posets
Jun
21
comment Defining principal elements of every poset. Is this a new idea?
@OlivierBégassat: Thanks, corrected
Jun
20
comment Writing a chain of implications in English
@DanPiponi: A reader may be misguided (especially when we say "four assertions") by the fact that the last (fourth) "assertion" is supposed to imply an empty set of "following ones"
Jun
20
comment Writing a chain of implications in English
@DanPiponi: Will "Each of these assertions implies the following ones:" before a numbered list clear by itself (even for beginning students)? Or does this need further clarification?
Jun
20
comment Writing a chain of implications in English
Hm, I may write "The following is a tuple of implications: (1) ... (2) ... (3) ... (4) ..." and define "tuple of implications" near the beginning if my book (as a tuple of logical formulas, every of which (except of the last) implies the next)
Jun
20
comment Writing a chain of implications in English
Saying it one time wouldn't insult. But I want to repeat it in many (maybe around 50, I haven't calculated) theorems in the book I write. Repeating this phrase every time would be not good