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1.
Idealization of a decomposition theorem 总被引:1,自引:1,他引:0
In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A
I-sets and A
I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A
I-continuous.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
Remo V. Hügli 《Integral Equations and Operator Theory》2011,70(1):101-123
It is shown that if P is a weak*-continuous projection on a JBW*-triple A with predual A
*, such that the range PA of P is an atomic subtriple with finite-dimensional Cartan-factors, and P is the sum of coordinate projections with respect to a standard grid of PA, then P is contractive if and only if it commutes with all inner derivations of PA. This provides characterizations of 1-complemented elements in a large class of subspaces of A
* in terms of commutation relations. 相似文献
3.
B. Al-Nashef 《Acta Mathematica Hungarica》2002,97(1-2):115-120
The following two decomposition theorems are obtained. (1) A function f is α-continuous if and only if f is pre-continuous and αα-continuous, (2) A function f is semi-continuous if and only if f is spr-continuous and αLC-continuous.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
First, we introduce the notion of f
I-sets and investigate their properties in ideal topological spaces. Then, we also introduce the notions of R
I
C-continuous, f
I-continuous and contra*-continuous functions and we show that a function f: (X,τ,I) to (Y,φ) is R
I
C -continuous if and only if it is f
I-continuous and contra*-continuous.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
We show that if A is a simply connected, finite, pointed CW-complex, then the mapping spaces Map*(A,X) are preserved by the localization functors only if A has the rational homotopy type of a wedge of spheres V
l
S
k
. 相似文献
6.
7.
Hua-Ping Yu 《代数通讯》2013,41(6):2187-2197
An associative ring R with identity is said to have stable range one if for any a,b? R with aR + bR = R, there exists y ? R such that a + by is left (equivalently, right) invertible. The main results of this note are Theorem 2: A left or right continuous ring R has stable range one if and only if R is directly finite (i.e xy = 1 implies yx = 1 for all x,y ? R), Theorem 6: A left or right N 0o-quasi-continuous exchange ring has stable range one if and only if it is directly finite, and Theorem 12: left or right N 0-quasi-continuous strongly π-regular rings have stable range one. Theorem 6 generalizes a well-known result of Goodearl [10], which says that a directly finite, right N o-continuous von Neumann regular ring is unit-regular 相似文献
8.
Gary Chartrand Elzbieta B. Jarrett Farrokh Saba Ebrahim Salehi Ping Zhang 《Czechoslovak Mathematical Journal》2001,51(2):351-361
For a nontrivial connected graph F, the F-degree of a vertex in a graph G is the number of copies of F in G containing . A graph G is F-continuous (or F-degree continuous) if the F-degrees of every two adjacent vertices of G differ by at most 1. All P3-continuous graphs are determined. It is observed that if G is a nontrivial connected graph that is F-continuous for all nontrivial connected graphs F, then either G is regular or G is a path. In the case of a 2-connected graph F, however, there always exists a regular graph that is not F-continuous. It is also shown that for every graph H and every 2-connected graph F, there exists an F-continuous graph G containing H as an induced subgraph. 相似文献
9.
Anna Draganova 《Czechoslovak Mathematical Journal》2009,59(1):51-60
For any nontrivial connected graph F and any graph G, the F-degree of a vertex v in G is the number of copies of F in G containing v. G is called F-continuous if and only if the F-degrees of any two adjacent vertices in G differ by at most 1; G is F-regular if the F-degrees of all vertices in G are the same. This paper classifies all P
4-continuous graphs with girth greater than 3. We show that for any nontrivial connected graph F other than the star K
1,k
, k ⩾ 1, there exists a regular graph that is not F-continuous. If F is 2-connected, then there exists a regular F-continuous graph that is not F-regular.
相似文献
10.
J. K. Kohli 《Mathematische Nachrichten》1980,97(1):189-196
A topological space is called s-regular if each closed connected set and a point outside it are separated by disjoint open sets. Similarly notion of complete s-regularity is introduced; basic properties of s-regular spaces and completely s-regular spaces are studied and interrelations between them and the standard separation axioms are observed. It is shown that in the class of semilocally connected spaces s-regularity coincides with regularity and complete s-regularity coincides with complete regularity. Moreover, properties of s-continuous functions are studied and it is shown that s-regularity and completely s-regularity are preserved under certain s-continuous mappings. 相似文献