friday came. would on weekend continue topology study as usual.

hmm this weekend i think i could iterate on maths study wishfully for topology textbook side. hmm i bought some filter coffee machine (not expensive ones) and some roasted coffees types. but i think coffee type i liked most is not filter coffee but anyway i can turn it to espresso with adding water :) or could later buy espresso making machines. turned out coffee type i like most is made of espresso coffee type but not filter coffe. i saw this after i bought coffee machine either :) nevertheless i bought the same coffee brand that i liked roasted taste of.  i when drinking that coffee with no sugar no crema at all, it just tastes awesome. so i fgured out  capicunoe or coffee+crema that i have at home is not the coffee i like most. actually i just drink its because its coffee but not liking:D i think i like sole coffee with no crema or sugar. but for that i think coffee type matters alot. so very eagerly awaiting coffee machine i bought on thursday or wednesday i dont remmeber. i used pad coffee and definitely not liked its taste. usually i dont like also filter coffee. but i like hot water added espresso coffee as i checked my fav coffee type to see how its made. i think i bought the coffee machine on thursday. i wont drink much but would take at most 2 cups per day. i would continue overdrinking water (active o2) since h2o is healthier than coffee since coffee is diuertic i mean it reduces the water level in body. though coffee has also good side effects like its has even has antioxidants alot as far as i know. so it wouold be nice to replace this tasteless (or taste does not like coffee) this crema + coffee stuff i bought. it just tastes like hot water but no coffee taste happens from this. i definitely think i dont like coffee crema any :) but were using that because sole coffee were also impacitng alot my stomach. but i think i could manage water level to arrange  mixture level of coffee water that it wont have bad side effects to stomach (that which of mine has some sickness)  

so very eagerly awaiting filter coffee machine, the coffee blend i bought and wondering if it would any resemble startbucks coffee i liked most. recent one tasted very roasted. i liked that. so i tried to find its blend to buy in addition to coffee machine. to setup some such morning drink to myself to wake up. i wish i dont overdrink coffee either. nope i think i wont since i got used to drinking h20 alot recently. 

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has been a very busy week beside having failed in this week's business objectives. at work. yupp.  yayyy now weekend starts. so has been an epic failure at work type weekend since failed my goals and so schedule had to be extended due to my failure of accomplishing work jobs.so an epic failure type work week for me where i want to add face palm emoji to my failing to accomplish align to schedule. some troubles in some works  happent that i couldnt resolve during the week somewhow even if i tried alot. 

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anyway weekend started so its topology time :) actually last very evening i also studied in revising some chapters topics.  its so fun to sit on chair and think of topic i read to understand it correct. if one see from outsideif came to my flat,  would had think i am doing nothing and jhust sitting on chair whilst i am thinking of topology topic to understand some concept correct from phd textbooks chapters that i revise.its funny to use IDE of mind to try to understand phd textbook of some part what it meant. to get aligned with its meaning.  phd textbooks has side effect of taking brain process funnily like that:D i mean whilst i do look doing laziness (though i do alot laziness in weekends many times eihher) somcetimes its topology stuff thinking not laziness. or sometimes even if i rest in my bed, i just continue tio think of the textbook topic to reaffirm its understanding and theorem is correct. you got tbe creative in studying to this topics yourself. i mean to understand what they meant in some topic. 

for instance let me clarify one such topic:

e.g. in hausdorff spaces, every compact set is closed.

now. if you think you think this mumst be like this already when thinking of, i mean logically. but when you think things like:

ig. if you take a limit of p/q where q goes to infinite, and p/q denoting the lenght of a line strip among a line which lets think as our set. if this was a bounded line lets for instance think. normally you expect that if you go to infinity line strip legnth would come 0. but in real analysis we saw its considered not like that and considered as always having a remaining part if it were like mechanism to reduce lnies were done with set intersection and infinite intersection of covering sets. on a real line. that there p/q logic does not match up to the fact that there exists always some line part. which they call it as another reason for real numbers existence topics. 

so when you do construct such concentric sets of <A,alpha> <B, beta> where B is a subset of A and in such directed net (directed sdet) beta is greater than alpha, even with such notnation where a final net is tried to be reached, either frequential or eventual net, whichever one, you choose, you would see that the main topic of covering spaces and compactness becomes illogical at such reference frame. since the rational numbrs wise it would have empty neighbourhood such infinity type intersections. 

so when you cover a space with open subset covers, so the condition of every cover of the set being finitely counted,  becomes depending ona not supporting reference frame when if we reduce open neighbourhood radius of covering sets iteratively.  so in that sense,

lets come back to topic again, if a set is closed and hausdorff its compact right?

they tackle this coming from the outside the outside of the set should have no bounds and could be any value until the boundary of the set, so when its a closed set and open outside, it means with that finite sets inside the set covering it, and the intersection of their cmplements to reach up to the same definition's outside region, we end up with an oipen outside region which means the set it self must be closed.

but when coming to that nonsupportive reference fraame, where infinite subsets with zero neighbourhood radius, in that you have a nonsupportive referenbce frame where a compact set becomes also noncompact if we could consider the infintiy (zero radius)also as a valid definition.

so then one understands they dont include that problematic refernece frame, so then it becomes definitely having finite number of subsets.

so trying to understand theorems what they means takes time when you are autodidactively studying.   

e.g. same goes to the fact of every net has a universal subnet. that you think of in terms of infintiies with taking alpha to minus infinity mindset. and understand that in such negative horizion there must be some region of eventual type net region. 

i saw this weird infinity tackling mechanisms before also in author Resnick's such textbooks. 

this one used Dynkin's one theorem to setup a proof such a definition to prove that every net has a universal subnet. 

quite logical solution it had. considering the endlessness of inifinity.

so reference frames to tackle infinity topic seems very important in this studies i think. e.g. some approaches has devised real numbers support system to tackle those topics. but i also think this conceptual continuity desire comes from the fact that quantum mechanics were not present by the times these theorems were built. and it were not known by then nature (i mean physiucs) iterates with eigenvalues actually i mean there is no continuoity in logic of qm eigen value change. so this ontology structure or support systems represents reflects an era where quantum mechanics were not present so they are aligned wiht such thinking paradigms. 

so we need to be abel to create ontology structures that tackles infinity with also other possible definitions. though any definition of might had been invented already either. but at least ontology wise we dont need to follow previous ontologies in that. or making it generic at least i mean.

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ah i confused the theorem it were like every hausdorff and compact space is closed. 

its as you read intuitively you get to know already that an open ended set could have inifinte subcover. i mean intuitively it is kind of tacit quite alot. but not the intuition but wiht proof book proves coming from outside and showing the outside of such set must have no bound etc. 

maths could never depend on intuition even could be supported with since sometimes intuitioon might even return false resutl.

e.g. if you define A* B operation with sequences type convolution of A and B sequences, you would have in some times results not having exactly A Convolve B when you change the sequence order. again due to infinity topic. that i mean intuitive maths is not correct many times. but might be correct in alot other times either.

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so  i wish clear why i mentioned sitting on a chair and just thinking topology means :) 

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this project that is studied to on weekends mainluy and somedays on evenoings is also very urgent.l since i need to develop such nanobots based cancer healing tech asap since my dad has lung cancer though i think current medicine is also great in that topics but we also need to develop  nanobots type medicines plus  also  electron microscope like dna rna imaging devices to target nanobots to cancer cells effectively. yuppp. cancer's medicine tech currently is also very awesome. e.g.  keytruda medicine or intelligent targeted medicines.  both are very cool i think. also even mrna tech for cancer is also developed in tandem which would later in fture i guess turn cancer to flu like easily solvable chronic illness type. which is also cool. but in tandem before all i also want to develoip nanobot tech later after coder ai is developed to target cancer cells not with t cells but with nanobots. yupp.

but this all be later after coder ai is ready. first robots would be built to do build physics labs e.g. particle physics labs. to do device new medical devices for electron microscope type but non invasive type with other particles. or other tech. i dont know. somehow it would be figured out. all later. first coder ai project is what is most important is. 

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hmm still eagerly awaiting my coffee machine to taste that awesome coffee instead of this cream added unnice coffee. it tastes like hto water and no coffee at all. too much cream. nope didnt liked any.

last days one day i ordered from startbucks and i remembered how coffee is instead of cream added coffee. starbucks coffees are i think some of them really taste very good. though i am not coffee guru any either. imho lets say my opinion is that coffees i tried there tastes very good. 

i dont know if i would be able to make starbucks such coffee with filter machine, at least since i also bought starbucks coffee it might resemble but that coffee i like is not definitely filter coffee. though i wish it resdembles.:D 

cause everytime ordering from starbucks might turn out costly since every order has 10 euro limit and adding also tip etc.  i think not logical to order everyday since wouold mean at least 360 euros (and 2 euors tip) and plus i have to wait the coffee to come. so ordering seems not quite perfect option.  and i dont only order coffee i order also caloried stuff like cakes etc.

but i dont know if my coffee i would prepare at flat would any resemble that coffee i like alot at starbucks. i dont think so since it is not even filter coffee. but anyway filter coffee would be much better than the cream+coffee mixture or cappucino either. i both very dislike :D they dont taste like coffee at all. \\