Crystal 1. HαβεH HΓΔΣH; 2. H→H←H⇌H⇔H; 3. H—H═H≡H−H; 4. H∩H⊃H>≪H√H≡H±H; 5. {[(“H‘ah’a”H'sH′H)]};:,!?; 6. ◆⧫H▽H■H○·•● H△▲▽▼H□■H○●H◇◆H⧫◊H; 7. ØøŁłHÅß&*∗°H†‡§∫H%∏∑H€$; 9. ⓪0④4ⒷBⓌWⓓdⓔe; 10. spaces (space character placed between describing terms): regular space, thin space, no break space, narrow no break space; 11. ÖöÜüŸÿ1̈4̈Γ̈α̈∇̈ O̧o̧U̧u̧Y̧y̧1̧4̧Γ̧α̧∇̧ O̅o̅U̅u̅Y̅y̅1̅4̅Γ̅α̅∇̅ ỌọỤụỴỵ1̣4̣Γ̣α̣∇̣ ȎȏȖȗY̑y̑1̑4̑Γ̑α̑∇̑ 12. H∵…⋯H⋰H∬H∭H Structure

2007 ◽  
pp. 231-237
Author(s):  
Mandana Veiseh ◽  
Daniel Breadner ◽  
Jenny Ma ◽  
Natalia Akentieva ◽  
Rashmin C Savani ◽  
...  
Keyword(s):  
1969 ◽  
Vol 76 (2) ◽  
pp. 181 ◽  
Author(s):  
John Thomas

1994 ◽  
Vol 17 (4) ◽  
pp. 687-692 ◽  
Author(s):  
Martin M. Kovár

In this paper we studyθ-regularity and its relations to other topological properties. We show that the concepts ofθ-regularity (Janković, 1985) and point paracompactness (Boyte, 1973) coincide. Regular, strongly locally compact or paracompact spaces areθ-regular. We discuss the problem when a (countably)θ-regular space is regular, strongly locally compact, compact, or paracompact. We also study some basic properties of subspaces of aθ-regular space. Some applications: A space is paracompact iff the space is countablyθ-regular and semiparacompact. A generalizedFσ-subspace of a paracompact space is paracompact iff the subspace is countablyθ-regular.


2021 ◽  
Vol 13 (2) ◽  
pp. 292-304
Author(s):  
Ali Barzanouni ◽  
Ekta Shah

Abstract We study the notion of expansive homeomorphisms on uniform spaces. It is shown that if there exists a topologically expansive homeomorphism on a uniform space, then the space is always a Hausdor space and hence a regular space. Further, we characterize orbit expansive homeomorphisms in terms of topologically expansive homeomorphisms and conclude that if there exist a topologically expansive homeomorphism on a compact uniform space then the space is always metrizable.


Author(s):  
Hind Fadhil Abbas

The fusion of technology and science is a very complex and scientific phenomenon that still carries mysteries that need to be understood. To unravel these phenomena, mathematical models are beneficial to treat different systems with unpredictable system elements. Here, the generalized intuitionistic fuzzy ideal is studied with topological space. These concepts are useful to analyze new generalized intuitionistic models. The basic structure is studied here with various relations between the generalized intuitionistic fuzzy ideals and the generalized intuitionistic fuzzy topologies. This study includes intuitionistic fuzzy topological spaces (IFS); the fundamental definitions of intuitionistic fuzzy Hausdorff space; intuitionistic fuzzy regular space; intuitionistic fuzzy normal space; intuitionistic fuzzy continuity; operations on IFS, the compactness and separation axioms.


1972 ◽  
Vol 24 (2) ◽  
pp. 286-292 ◽  
Author(s):  
R. M. Stephenson

Throughout this paper all hypothesized spaces are T1. A regular space is called R-closed[11](regular-closed [7] or, equivalently, regular-complete [2]) provided that it is a closed subset of any regular space in which it can be embedded. A regular space (X, ℐ) is called minimal regular [2; 4] if there exists no regular topology on X which is strictly weaker than J. We shall call a regular space X strongly minimal regular provided that each point x ∈ X has a fundamental system of neighbourhoods such that for every V ∈ , X\V is an R-closed space.In §2 we note that a strongly minimal regular space is minimal regular, but we do not know if the converse holds. M. P. Berri and R. H. Sorgenfrey [4] proved that a minimal regular space is R-closed, and Horst Herrlich [7] gave an example of an R-closed space that is not minimal regular.


1989 ◽  
Vol 32 (4) ◽  
pp. 417-424 ◽  
Author(s):  
Ivan Baggs

AbstractAn example is given of a regular space on which every real-valued function with a closed graph is constant. It was previously known that there are regular spaces on which every continuous function is constant. It is also shown here that there are regular spaces that support only constant real-valued continuous functions, but support non-constant real-valued functions with a closed graph.


1990 ◽  
Vol 110 (2) ◽  
pp. 115-116 ◽  
Author(s):  
Hans-Peter A. K�nzi

Author(s):  
V. V. Mykhaylyuk

A connection between the separability and the countable chain condition of spaces withL-property (a topological spaceXhasL-property if for every topological spaceY, separately continuous functionf:X×Y→ℝand open setI⊆ℝ,the setf−1(I)is anFσ-set) is studied. We show that every completely regular Baire space with theL-property and the countable chain condition is separable and constructs a nonseparable completely regular space with theL-property and the countable chain condition. This gives a negative answer to a question of M. Burke.


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