The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “The power set of ω Elementary submodels and weakenings of CH”

Preservation of properties of a map by forcing

Akira Iwasa (2022)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let f : X Y be a continuous map such as an open map, a closed map or a quotient map. We study under what circumstances f remains an open, closed or quotient map in forcing extensions.

The subspace of weak P -points of *

Salvador García-Ferreira, Y. F. Ortiz-Castillo (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let W be the subspace of * consisting of all weak P -points. It is not hard to see that W is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that W is a p -pseudocompact space for all p * .

The cleanness of (symbolic) powers of Stanley-Reisner ideals

Somayeh Bandari, Ali Soleyman Jahan (2017)

Czechoslovak Mathematical Journal

Similarity:

Let Δ be a pure simplicial complex on the vertex set [ n ] = { 1 , ... , n } and I Δ its Stanley-Reisner ideal in the polynomial ring S = K [ x 1 , ... , x n ] . We show that Δ is a matroid (complete intersection) if and only if S / I Δ ( m ) ( S / I Δ m ) is clean for all m and this is equivalent to saying that S / I Δ ( m ) ( S / I Δ m , respectively) is Cohen-Macaulay for all m . By this result, we show that there exists a monomial ideal I with (pretty) cleanness property while S / I m or S / I ( m ) is not (pretty) clean for all integer m 3 . If dim ( Δ ) = 1 , we also prove that S / I Δ ( 2 ) ( S / I Δ 2 ) is clean if and only...

On the compositum of all degree d extensions of a number field

Itamar Gal, Robert Grizzard (2014)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We study the compositum k [ d ] of all degree d extensions of a number field k in a fixed algebraic closure. We show k [ d ] contains all subextensions of degree less than d if and only if d 4 . We prove that for d > 2 there is no bound c = c ( d ) on the degree of elements required to generate finite subextensions of k [ d ] / k . Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of d , but that one can take c = d when d is prime. This question was inspired by work of...

On butterfly-points in β X , Tychonoff products and weak Lindelöf numbers

Sergei Logunov (2022)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let X be the Tychonoff product α < τ X α of τ -many Tychonoff non-single point spaces X α . Let p X * be a point in the closure of some G X whose weak Lindelöf number is strictly less than the cofinality of τ . Then we show that β X { p } is not normal. Under some additional assumptions, p is a butterfly-point in β X . In particular, this is true if either X = ω τ or X = R τ and τ is infinite and not countably cofinal.

The linear syzygy graph of a monomial ideal and linear resolutions

Erfan Manouchehri, Ali Soleyman Jahan (2021)

Czechoslovak Mathematical Journal

Similarity:

For each squarefree monomial ideal I S = k [ x 1 , ... , x n ] , we associate a simple finite graph G I by using the first linear syzygies of I . The nodes of G I are the generators of I , and two vertices u i and u j are adjacent if there exist variables x , y such that x u i = y u j . In the cases, where G I is a cycle or a tree, we show that I has a linear resolution if and only if I has linear quotients and if and only if I is variable-decomposable. In addition, with the same assumption on G I , we characterize all squarefree monomial ideals...

Relative weak derived functors

Panneerselvam Prabakaran (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let R be a ring, n a fixed non-negative integer, 𝒲 the class of all left R -modules with weak injective dimension at most n , and 𝒲 the class of all right R -modules with weak flat dimension at most n . Using left (right) 𝒲 -resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that - - is right balanced on R × R by 𝒲 × 𝒲 , and investigate the global right 𝒲 -dimension of R by right derived functors of .

On affinity of Peano type functions

Tomasz Słonka (2012)

Colloquium Mathematicae

Similarity:

We show that if n is a positive integer and 2 , then for every positive integer m and for every real constant c > 0 there are functions f , . . . , f n + m : such that ( f , . . . , f n + m ) ( ) = n + m and for every x ∈ ℝⁿ there exists a strictly increasing sequence (i₁,...,iₙ) of numbers from 1,...,n+m and a w ∈ ℤⁿ such that ( f i , . . . , f i ) ( y ) = y + w for y x + ( - c , c ) × n - 1 .

A note on the multiplier ideals of monomial ideals

Cheng Gong, Zhongming Tang (2015)

Czechoslovak Mathematical Journal

Similarity:

Let 𝔞 [ x 1 , ... , x n ] be a monomial ideal and 𝒥 ( 𝔞 c ) the multiplier ideal of 𝔞 with coefficient c . Then 𝒥 ( 𝔞 c ) is also a monomial ideal of [ x 1 , ... , x n ] , and the equality 𝒥 ( 𝔞 c ) = 𝔞 implies that 0 < c < n + 1 . We mainly discuss the problem when 𝒥 ( 𝔞 ) = 𝔞 or 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 for all 0 < ε < 1 . It is proved that if 𝒥 ( 𝔞 ) = 𝔞 then 𝔞 is principal, and if 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 holds for all 0 < ε < 1 then 𝔞 = ( x 1 , ... , x n ) . One global result is also obtained. Let 𝔞 ˜ be the ideal sheaf on n - 1 associated with 𝔞 . Then it is proved that the equality 𝒥 ( 𝔞 ˜ ) = 𝔞 ˜ implies that 𝔞 ˜ is principal.

On the hyperspace C n ( X ) / C n K ( X )

José G. Anaya, Enrique Castañeda-Alvarado, José A. Martínez-Cortez (2021)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let X be a continuum and n a positive integer. Let C n ( X ) be the hyperspace of all nonempty closed subsets of X with at most n components, endowed with the Hausdorff metric. For K compact subset of X , define the hyperspace C n K ( X ) = { A C n ( X ) : K A } . In this paper, we consider the hyperspace C K n ( X ) = C n ( X ) / C n K ( X ) , which can be a tool to study the space C n ( X ) . We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility. ...