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An amateur general topology researcher.


Aug
26
comment Directed multigraph with numbered edges
@Casteels: Accordingly my understanding "edge-labeled directed multigraph" may have labels which are not natural numbers, have duplicate labels for two different edges starting in the same vertex, etc. So, I think this is not an answer
Aug
23
comment A conjecture about filters and finite unions of cartesian products
No, not that simple. I keep thinking
Aug
23
comment A conjecture about filters and finite unions of cartesian products
It seems that there is a simple solution: Just restrict for the case when $a$ are trivial ultrafilters. No I am checking that this is a correct solution.
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"