... projective spaces of order 2 and all nâdimensional projective spaces with n+1 a power of 2, admit a parallelism (Baker. [1], Buetelspacher [2], Denniston [10]).
the Cartan formula for secondary operations, [7], and a particular factorization of the cube of a certain 8-dimensional cohomology class,. [10], to show that Hl5{X) ...
In other words, we have to consider N = 2 superconformal theory living on the world-sheet and ... the complex orthogonal group and (C* denotes the group of non-zero complex numbers. ... define a field of type Ton the superconformal manifold as a fc-c
An affine Î-domain of type A as above was studied by Russell [8] and Sathay e ... SIMPLE BIRATIONAL EXTENSIONS OF A POLYNOMIAL RING k[x,y]. 665. P2:=Ï{(F) ..... stands for a free Z-module of rank r nis the number of distinct irreducible ...
Jun 14, 1983 - We call A a strongly separable extension of R if A\otimes_{R}A\cong K\oplus L, where Hom_{A .... center C of A is contained in R. Then \Delta.
The result was conjectured by Serre in a letter to the first named author. This case however was left open in [5] and in CGS, while the extension groups of ...
associated with an irreducible representation $\delta$ .... $C^{\infty}(\Sigma)=\sum_{m,n\geq 0}\ovalbox{\tt\small REJECT}^{m}(R^{dp})\otimes\ovalbox{\tt\small ..... $=\frac{1}{\pi}\int_{-\pi/2}^{\pi/2}(\cos\theta)^{\lambda}e^{-il\theta}d\theta$.
PAUL F. DUVALL, PETER FLETCHER AND ROBERT A. MCCOY. This paper ..... P. Fletcher and R. L. Snider, Topological Galois spaces, Fund. Math., 68 (1970) ...
Mathematics. S(α) SPACES AND REGULAR HAUSDORFF EXTENSIONS. JACK RAY PORTER AND CHARLES I. VOTAW. Vol. 45, No. 1. September 1973 ...
studied in detail by E. Hille and R. Phillips [1] and R. A. Rosenbaum. [2]. ... author is indebted to Professor John Green for his guidance in its preparation. Thanks ...
all maximal dissipative, maximal accretive and self-adjoint extensions of such a ... The theory of extensions of symmetric operators is one of the main branches.
Nov 28, 2005 - Key words and phrases: Categorical groups, semidirect product, split ...... [17] A. R. Garzón and A. del Rıo, The Whitehead categorical group of ...
Jun 29, 1998 - Î(q( + q2) â A(q\ + q2); in this equality the right side is the difference of two ... in Kc, the same argument shows that there exists a bounded ...
Jul 7, 2012 - Vries operator 3 on its de Vries algebra of regular open sets, a lower .... B satisfying (i) 30=0 and (ii) 3(a∨b)=3a∨3b for each a,b∈B. For modal ...
Let H be a topological group, and let K be a discrete central subgroup of H. Let r .... By our above proposition, an abstract split of the given group extension ... G. Hochschild, The structure of Lie groups, Holden-Day, San Francisco, 1965. 2.
Feb 23, 1984 - hyperbolicity introduced by Ehrenpreis [4, Theorem 2] for Schwartz dis- ..... Paley-Weiner theorem to e D and using (17), it follows that the ...
Nov 17, 1995 - Let Y(t) (teRN) be a real-valued, centered Gaussian random field with y(0) = 0. We assume that Y(ή (ίeRN) has stationary increments and ...
These are all elements of A. It is easy to see that. (3.1.iii) p ..... pap by uniqueness or polar decompositions. A direct calculation shows that a has the form with u.
Oct 3, 2005 - MAR IA J. RIVERA ... see, this extension carries new problems, the solution of which is here ... From the Bartle-Dunford-Schwartz theorem, ... With respect to the Banach lattices theory we refer to [8, 11]. We ... 2. Spaces of (Φ )-qua
with an Appendix by Mark Dickinson & Krishnan Shankar. Introduction ...... manifolds, smoothings, and triangulations (with notes by John Milnor and. Michael ...
Dec 4, 1991 - the blow up of A, the unfolding (in fact, the resolution of singularities of ..... fact that the family {C face of A/C c (dim C)-skeleton of V} is totally.
DAVID P. BELLAMY. "Continuum" denotes a ..... 3 (1960), 421-428. 5. J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., (1969). 6.
Aug 16, 1995 - (c) reG4)p. A4p. (d) Sut(p) is an analytic Banach homogeneous space under the action ofGut and an analytic submanifold of. (e) /gut(p) is a C ...
Sep 1, 1995 - Denote a Banach space X equipped with the topology induced by ...... spaces with K Valdivia compact, WCD-spaces and all duals of Asplund.
A topological property & is called a Hausdorff extension property if each Hausdorff space X can be densely embedded in a space κ&Xsuch that (1) κ&X is a ...
PACIFIC JOURNAL OF MATHEMATICS Vol. 103, No. 1, 1982
EXTENSIONS OF HAUSDORFF SPACES JACK R. PORTER AND R. GRANT WOODS
A topological property & is called a Hausdorff extension property if each Hausdorff space X can be densely embedded in a space κ&X such that (1) κ&X is a Hausdorff space with property &9 (2) if 7 is a Hausdorff extension of X with -&*9 then there is a continuous function / = tc&X —> Y such that f(x) — x for each x e X, and (3) if X is iϊ-closed, then K&X—X. Both necessary conditions and sufficient conditions are given to characterize Hausdorff extension properties. Certain types of Hausdorff extension properties are shown to divide into classes such that each class has a largest member. In the latter part of the paper, for a Hausdorff extension property Z and f:Z->T are continuous and extend the identity map on X then:
EXTENSIONS OF HATJSDORFF SPACES (a)
f°g\χ
113
= lYtT.
(b) g is a homeomorphism from Y onto g[Y] that fixes X pointwise. Two extensions Y and Z of X are equivalent if there is a homeomorphism from Y onto Z that leaves X pointwise fixed. This is an "equivalence relation" on the class of extensions of X. Henceforth we identify equivalent extensions of a space. With this identification the class $?(X) of extensions of X is a set. We next define a partial order on DEFINITION 1.3. (a) Let Y and Z be extensions of X Then Y is projectively larger than Z (denoted Y ^ Z) if there is continuous function from Y to Z that fixes X pointwise. (b) Let y be a set of extensions of X An extension Y of X is a projective maximum for Sf if Y e Sf and Y ^ Z for all ZeS^.
It is well-known (see, for example, [15]), and follows from 1.2, that ί?(-X") is partially ordered by ^ . A major theme of this paper is to investigate those topological properties & for which the set of ^-extensions of X has a projective maximum. We give examples of such properties below (see 2.3). 1.4. A filter (resp. filter base) on the lattice of open sets of X is called an open filter (resp. open filter base) on X A maximal (with respect to set inclusion) element in the set of open filters on X is called an open ultra filter. The set Π fax F: Fe ^} is called the adherence (in X) of the open filter base ^~, and is denoted adxG^H An open filter base ^ on X is fixed if ad z (^~) Φ 0; otherwise it is free. DEFINITION
DEFINITION 1.5. A space X is H-closed if X is closed in each Hausdorff space in which it is embedded. The set of ίf-closed extensions of X will be denoted by
The following characterizations of H-closed spaces will be useful; see, for example, problems YIK and ΠL of Willard [19]. 1.6. The following are equivalent for a space X: X is H-closed. Each open ultra filter on X is fixed. Each open filter on X is fixed. // ^ is an open cover of X there is a finite subfamily such that \J ^ is dense in X
