Higson have introduced the conception of "Higson’s corona" (see [1]). For a given metric space X, it is a kind of compactification of X related to the metric d on it. Denote by BR(X) the set {y ∈ X\d(x,y) ...Higson have introduced the conception of "Higson’s corona" (see [1]). For a given metric space X, it is a kind of compactification of X related to the metric d on it. Denote by BR(X) the set {y ∈ X\d(x,y) < R}. Recall that a slowly oscillating function on X is a function f G C*(X) satisfying the following condition:展开更多
Necessary and sufficient conditions are studied that a bounded operator Tx =（x1^＊x, x2^＊x,…） on the space e∞, where xn^＊∈e∞^＊, is lower or upper semi-Fredholm; in particular, topological properties of the se...Necessary and sufficient conditions are studied that a bounded operator Tx =（x1^＊x, x2^＊x,…） on the space e∞, where xn^＊∈e∞^＊, is lower or upper semi-Fredholm; in particular, topological properties of the set {x1^＊, x2^＊ …} are investigated. Various estimates of the defect d（T） = codim R（T）, where R（T） is the range of T, are given. The case of xn^＊ = dnxtn^＊,where dn ∈ R and xtn^＊ 〉 0 are extreme points of the unit ball Be∞^＊, that is, tn ∈ βN, is considered. In terms of the sequence {tn}, the conditions of the closedness of the range R（T） are given and the value d（T） is calculated. For example, the condition {n ： 0 〈 ｜da｜ 〈 δ}= θ for some 5 is sufficient and if for large n points tn are isolated elements of the sequence {tn}, then it is also necessary for the closedness of R（T） （tn0 is isolated if there is a neighborhood U of tno satisfying tn ∈ U for all n ≠ n0）. If {n ： ｜dn｜ 〈 δ} = θ, then d（T） is equal to the defect δ{tn} of {tn}. It is shown that if d（T） = ∞ and R（T） is closed, then there exists a sequence {An} of pairwise disjoint subsets of N satisfying XAn ∈ R（T）.展开更多
In this paper,the following results are obtained: (1) The Sorgenfrey Line is a non-Br-space; (2) We introduce Well-distributed complete spaces and locally Cech complete spaces andprove both the two classes of spacs ar...In this paper,the following results are obtained: (1) The Sorgenfrey Line is a non-Br-space; (2) We introduce Well-distributed complete spaces and locally Cech complete spaces andprove both the two classes of spacs are Br-spaces. The first result shows that there is the non-Br-space which is paracompact, Lindelof and complete quasi-metric. The second result generalizes theByczowski &. Pol theorem(i. e. Cech-complete spaces are Br-spaces) in two aspects.展开更多
In this paper,we present that if Y is a hereditarily metacompact space and{Xn：n∈ω}is a countable collection of Cech-scattered metacompact spaces,then the followings are∏equivalent：（1）Y×∏n∈ωXn is metacom...In this paper,we present that if Y is a hereditarily metacompact space and{Xn：n∈ω}is a countable collection of Cech-scattered metacompact spaces,then the followings are∏equivalent：（1）Y×∏n∈ωXn is metacompact,（2）Y×∏n∈ωXn is countable metacompact,（3）Y×n∈ωXn is orthocompact.Thereby,this result generalizes Theorem 5.4 in[Tanaka,Tsukuba.J.Math.,1993,17：565–587].In addition,we obtain that if Y is a hereditarilyσ-metacompact space and{Xn：n∈ω∏}is a countable collection of Cech-scatteredσ-metacompact spaces,then the product Y×n∈ωXn isσ-metacompact.展开更多
By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding...By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding Y as a dense subspace of , YS = {ε |ε is an open CD*-filter that does not converge in Y}, YT = {A|A is a basic open CD*-filter that does not converge in Y}, is the topology induced by the base B = {U*|U is open in Y, U ≠φ} and U* = {F∈Ysw (or YTw)|U∈F}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space X?can be obtained from a by the?similar process in Sec.3.展开更多
This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived...This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.展开更多
文摘Higson have introduced the conception of "Higson’s corona" (see [1]). For a given metric space X, it is a kind of compactification of X related to the metric d on it. Denote by BR(X) the set {y ∈ X\d(x,y) < R}. Recall that a slowly oscillating function on X is a function f G C*(X) satisfying the following condition:
文摘Necessary and sufficient conditions are studied that a bounded operator Tx =（x1^＊x, x2^＊x,…） on the space e∞, where xn^＊∈e∞^＊, is lower or upper semi-Fredholm; in particular, topological properties of the set {x1^＊, x2^＊ …} are investigated. Various estimates of the defect d（T） = codim R（T）, where R（T） is the range of T, are given. The case of xn^＊ = dnxtn^＊,where dn ∈ R and xtn^＊ 〉 0 are extreme points of the unit ball Be∞^＊, that is, tn ∈ βN, is considered. In terms of the sequence {tn}, the conditions of the closedness of the range R（T） are given and the value d（T） is calculated. For example, the condition {n ： 0 〈 ｜da｜ 〈 δ}= θ for some 5 is sufficient and if for large n points tn are isolated elements of the sequence {tn}, then it is also necessary for the closedness of R（T） （tn0 is isolated if there is a neighborhood U of tno satisfying tn ∈ U for all n ≠ n0）. If {n ： ｜dn｜ 〈 δ} = θ, then d（T） is equal to the defect δ{tn} of {tn}. It is shown that if d（T） = ∞ and R（T） is closed, then there exists a sequence {An} of pairwise disjoint subsets of N satisfying XAn ∈ R（T）.
文摘In this paper,the following results are obtained: (1) The Sorgenfrey Line is a non-Br-space; (2) We introduce Well-distributed complete spaces and locally Cech complete spaces andprove both the two classes of spacs are Br-spaces. The first result shows that there is the non-Br-space which is paracompact, Lindelof and complete quasi-metric. The second result generalizes theByczowski &. Pol theorem(i. e. Cech-complete spaces are Br-spaces) in two aspects.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(Grant No.14ZB0007)
文摘In this paper,we present that if Y is a hereditarily metacompact space and{Xn：n∈ω}is a countable collection of Cech-scattered metacompact spaces,then the followings are∏equivalent：（1）Y×∏n∈ωXn is metacompact,（2）Y×∏n∈ωXn is countable metacompact,（3）Y×n∈ωXn is orthocompact.Thereby,this result generalizes Theorem 5.4 in[Tanaka,Tsukuba.J.Math.,1993,17：565–587].In addition,we obtain that if Y is a hereditarilyσ-metacompact space and{Xn：n∈ω∏}is a countable collection of Cech-scatteredσ-metacompact spaces,then the product Y×n∈ωXn isσ-metacompact.
文摘By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding Y as a dense subspace of , YS = {ε |ε is an open CD*-filter that does not converge in Y}, YT = {A|A is a basic open CD*-filter that does not converge in Y}, is the topology induced by the base B = {U*|U is open in Y, U ≠φ} and U* = {F∈Ysw (or YTw)|U∈F}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space X?can be obtained from a by the?similar process in Sec.3.
文摘This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.
