National Top Stream

Report. "

Turning around beautifully, Zhuang Weiran began to write on the blackboard, "My academic lecture today is mainly about topological linear spaces in the field of functional analysis."

【…

In the 20s, katsaraska and liudb [70] first proposed the concept of fuzzy topological linear space using changcl's fuzzy topology, but because the topology in the definition does not have "translation invariance", subsequent work cannot continue. In 1, Katsaras changed the original fuzzy topology into the fuzzy topology in the lowenr sense, and redefined the fuzzy topological linear space.

……

Suppose x is a linear space on the number field k, if the i-fuzzy topological space (x, t) satisfies the following conditions:

(l1)?xλ, yμ∈t(ix), a?∈f(x)

……

If (x, t) is an i-fuzzy topological linear space, qxλ is the i-fuzzy heavy domain system of xλ, ?xλ, yμ∈t(ix)

……

If qθλ is the zero-element multi-field system of the i-fuzzy topological linear space (x, t), then

(e1)?a?,?a?∈qθλ→θλq?a?

(e2)?a?,b?,?(a?∈qθλ)∧(b?∈qθλ)→(a?∧b?)∈qθλ

……5】

Zhuang Weiran kept writing calculation formulas on the blackboard, and Chen Xinyao could understand them at first, but half-understood in the middle, and almost couldn't understand them afterwards.

Chen Xinyao basically represented most of the people present, and everyone frowned tightly, knowing that the academic lecture of this big boss would definitely not be easy.But it is so difficult to understand, it is really a headache.If at the beginning it was considered simple and easy to understand, then in the middle and late stages, it is simply incomprehensible.

Some things are not because Zhuang Weiran doesn't want to explain in a simple way, but because they are too in-depth. They don't have so much knowledge reserve, so they don't understand at all.

He Zhenguo had already started to feel drowsy, Zhuang Weiran stopped writing, "Today, I will talk about this."

"Anyone want to ask questions?"

Schultz raised his hand, Zhuang Weiran said with a light smile, "Mr. Schultz, please."

"I would like to ask Professor Zhuang to talk about the issue of σ being i-fuzzy balance."

"No problem." Zhuang Weiran pushed the blackboard away and erased the words written on the blackboard just now——

【…

Suppose x is a linear space on the number field k, q≤σ is the normal i-fuzzy subset family on f(x), if q satisfies (e22), (e1), (e2) and (e3) in Theorem 5 ), then there exists a unique i-fuzzy topology t on x

In particular, if q also satisfies (e4), (e6) and (e7), then (x, t) is an i-fuzzy topological linear space, and q is a balanced heavy field system with respect to the zero element θλ of t.

Proof First we let a?∈t:=(?xλ)(xλq?a?→(?b?)(b?∈q∧xb?≤a?)), then it is easy to prove that t is an i-fuzzy on x Topology, the following needs to prove that q is an i-fuzzy balanced heavy field system with respect to the zero element θλ of t and (x, t) is an i-fuzzy topological linear space.

If q also satisfies (e4), (e6) and (e7), then qxλ is the i-fuzzy heavy domain system of any fuzzy point xλ in (x, t), here we set a?∈qxλ:=a??x ∈q

……6】

"In this case, can Mr. Schultz be clearer?"

"It's very clear." Schultz sat down, Zhuang Weiran looked at everyone again, "So, does anyone else have any different ideas?"

"No more?" After Zhuang Weiran asked several times in a row, no one spoke, he could only say with a smile, "If everyone has no idea, then today's academic lecture will be over." Cleaned up his Things, when Zhuang Weiran didn't leave, no one moved.Obviously to show respect for Zhuang Weiran, after he leaves, the others will leave.

Just as Zhuang Weiran turned around and left the academic lecture hall, the others stood up.Faltins also followed in Zhuang Weiran's footsteps, "Zhuang."

"Professor Faltings." Zhuang Weiran turned his head, looked at Faltings and asked with a smile, "Mr. Faltings, what do you want?"

"I just heard from Schultz that you seem to be very interested in the Millennium Prize problem?"

"Probably." Zhuang Weiran smiled awkwardly, "Actually, there is nothing special about it, I just want to challenge whether I can continue to get the scholarship from the Cray Mathematics Institute."

Since this matter has to be known sooner or later, it is better for him to admit it openly.

"Are you short of money?" Faltings looked at Zhuang Weiran in disbelief, a genius mathematician like him.In this era, it is simply impossible to be short of money.

"..." Zhuang Weiran didn't know how to answer Faltings, so he could only laugh awkwardly.

If he hadn't invested in the laboratory, how could he be so short of money.

"Zhuang, are you really short?" Faltins' voice was full of surprise, it was impossible, he was almost a chair professor at Princeton University, how could he be short of money.This is absolutely impossible, so strange.

"No." Zhuang Weiran shook his head hurriedly and said, "I'm really just curious, how many times I can get the Cray Mathematics Institute's bonus, that's all."

Zhuang Weiran hastily denied it, no one believed that as a genius mathematician, he was so short of money that he wanted to continue to earn money from the Clay Institute of Mathematics.

Although it is true that he is very short of money, there is no need to make it known to everyone, just say that he wants to continue to do the Millennium Prize puzzle.I believe that Mr. Faltings should not continue to speculate elsewhere.

Faltings looked at Zhuang Weiran for a long time, but in the end he still didn't understand what Zhuang Weiran was thinking.He could only ponder and say, "Zhuang, have you made your decision?"