ALMOST GP-SPACES

Title & Authors
ALMOST GP-SPACES

Abstract
A T$\small{_1}$ topological space X is called an almost GP-space if every dense G$\small{_{\delta}}$-set of X has nonempty interior. The behaviour of almost GP-spaces under taking subspaces and superspaces, images and preimages and products is studied. If each dense G$\small{_{\delta}}$-set of an almost GP-space X has dense interior in X, then X is called a GID-space. In this paper, some interesting properties of GID-spaces are investigated. We will generalize some theorems that hold in almost P-spaces.
Keywords
weakly Volterra space;G$\small{{\delta}}$-filter;almost GP-space;GID-space;almost P-space;
Language
English
Cited by
1.
Gδ-Blumberg spaces, Filomat, 2010, 24, 4, 129
2.
Spaces in which every dense subset is aGδ, Quaestiones Mathematicae, 2016, 39, 2, 251
3.
An Algebraic Characterization of Blumberg Spaces, Quaestiones Mathematicae, 2010, 33, 2, 223
References
1.
M. R. Ahmadi Zand, Algebraic characterization of Blumberg spaces, in progress

2.
F. Azarpanah, On almost P-spaces Far East J. Math. Sci. (FJMS) 2000, Special Volume, Part I, 121-132

3.
J. Cao and D. Gauld, Volterra spaces revisited, J. Aust. Math. Soc. 79 (2005), no. 1, 61-76

4.
J. Cao and H. J. K. Junnila, When is a Volterra space Baire?, Topology Appl. 154 (2007), no. 2, 527-532

5.
F. Dashiell, A. Hager, and M. Henriksen, Order-Cauchy completions of rings and vector lattices of continuous functions, Canad. J. Math. 32 (1980), no. 3, 657-685

6.
R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989

7.
D. Gauld, S. Greenwood, and Z. Piotrowski, On Volterra spaces. II, Papers on general topology and applications (Gorham, ME, 1995), 169-173, Ann. New York Acad. Sci., 806, New York Acad. Sci., New York, 1996

8.
D. Gauld, S. Greenwood, and Z. Piotrowski, On Volterra spaces. III, Topological operations. Proceedings of the 1998 Topology and Dynamics Conference (Fairfax, VA). Topology Proc. 23 (1998), Spring, 167-182

9.
D. Gauld and Z. Piotrowski, On Volterra spaces, Far East J. Math. Sci. 1 (1993), no. 2, 209-214

10.
L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, 1976

11.
G. Gruenhage and D. Lutzer, Baire and Volterra spaces, Proc. Amer. Math. Soc. 128 (2000), no. 10, 3115-3124

12.
M. Henriksen, Spaces with a pretty base, J. Pure Appl. Algebra 70 (1991), no. 1-2, 81-87

13.
R. Levy, Almost-P-spaces, Canad. J. Math. 29 (1977), no. 2, 284-288

14.
J. Martinez and W. Wm. McGovern, When the maximum ring of quotients of C(X) is uniformly complete, Topology Appl. 116 (2001), no. 2, 185-198

15.
A. I. Veksler, P0-points, P0-sets, P0-spaces. A new class of order-continuous measures and functionals, Dokl. Akad. Nauk SSSR 212 (1973), 789-792

16.
R. C. Walker, The Ston- Cech Compactification, Springer Verlag, Mass, 1970

17.