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seen Oct 6 at 12:29

Apr
11
accepted If $X \times \{0\} \cup A \times I$ is closed in $X \times I$. Then, is $A$ closed in $X$?
Apr
11
comment If $X \times \{0\} \cup A \times I$ is closed in $X \times I$. Then, is $A$ closed in $X$?
Am I right in thinking that $B\times (0,1]$ is the complement of $X \times \{0\} \cup A \times I$ in $X \times I$. If it is true, then it follows that $B\times (0,1]$ is open.
Apr
11
comment Is the length of the composition series of a free module identical to the number of its bases?
It is the page 118 of 1969 version.
Apr
11
comment Is the length of the composition series of a free module identical to the number of its bases?
It works. Then, the description of the example in this famous book is not correct. Anyway, thank you for your help.
Apr
11
asked If $X \times \{0\} \cup A \times I$ is closed in $X \times I$. Then, is $A$ closed in $X$?
Apr
11
comment Is the length of the composition series of a free module identical to the number of its bases?
In the example, $A_n$ is the set of the homogeneous polynomials of degree $n$.
Apr
11
comment Is the length of the composition series of a free module identical to the number of its bases?
$A$ is a Noetherian graded ring $A=\oplus_{n=0}^\infty A_n$. $M$ is a finitely-generated graded $A$-module $M=\oplus_{n=0}^\infty M_n$.
Apr
11
revised Is the length of the composition series of a free module identical to the number of its bases?
added 4 characters in body
Apr
11
revised Is the length of the composition series of a free module identical to the number of its bases?
added 4 characters in body
Apr
11
asked Is the length of the composition series of a free module identical to the number of its bases?
Mar
25
comment If a chain of distinct irreducible closed subsets of a quasi-affine variety $Y$ is maximal, a chain of their closures is maximal in $\overline{Y}$?
Thank you again. I understand completely this time.
Mar
24
accepted If a chain of distinct irreducible closed subsets of a quasi-affine variety $Y$ is maximal, a chain of their closures is maximal in $\overline{Y}$?
Mar
24
comment If a chain of distinct irreducible closed subsets of a quasi-affine variety $Y$ is maximal, a chain of their closures is maximal in $\overline{Y}$?
Thank you for answering my question. I didn't notice that $W'$ is an open subset of W. One thing is not clear to me. You wrote $Z_i$ is not only irreducible in $Y$ but also in $X$. Does the irreducibility of a subset depend on the space containing it ?
Mar
22
asked If a chain of distinct irreducible closed subsets of a quasi-affine variety $Y$ is maximal, a chain of their closures is maximal in $\overline{Y}$?
Mar
7
awarded  Yearling
Mar
7
accepted Isomorphism of an extension field of a field of finite transcendence degree
Mar
7
asked Isomorphism of an extension field of a field of finite transcendence degree
Feb
5
answered If a neibourhood of the origin shrinks to the origin then its closure also shurinks to the origin?
Jan
31
accepted The kernel of homomorphism of a local ring into a field is its maximal ideal?
Jan
31
comment If a neibourhood of the origin shrinks to the origin then its closure also shurinks to the origin?
The definition in the book is as follows: $X$ is an F-space if its topology $\tau$ is induced by a complete invariant metric $d$.