De morgan on map colouring and the separation axiom

1983 ◽  
Vol 28 (2) ◽  
pp. 165-170
Author(s):  
N. L. Biggs
Keyword(s):  
Separation Axiom

scholarly journals A new separation axiom in grill topological spaces

2019 ◽  
Vol S (01) ◽  
pp. 706-709
Author(s):  
Maragatha Meenakshi P. ◽  
Chandran S.
Keyword(s):  
Topological Spaces ◽  
Separation Axiom

scholarly journals Topologies on Z n that Are Not Homeomorphic to the n-Dimensional Khalimsky Topological Space

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1072 ◽  
Author(s):  
Sang-Eon Han ◽  
Saeid Jafari ◽  
Jeong Kang
Keyword(s):  
Applied Sciences ◽  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Discrete Topology ◽  
Separation Axiom ◽  
Different Types

The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on Z n which are not homeomorphic to the typical n-dimensional Khalimsky topological space. Based on these different types of new topological structures on Z n , many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on.

A general theory of separation, regularity, and connectedness properties

1976 ◽  
Vol 80 (1) ◽  
pp. 81-90 ◽  
Author(s):  
D. M. G. McSherry
Keyword(s):  
General Theory ◽  
Regularity Conditions ◽  
Binary Relations ◽  
Separation Axiom ◽  
Separation Axioms ◽  
The Family

AbstractThe notion of basic topological binary relations is introduced, and corresponding to each such relation we define -regularity, -connectedness, and a separation axiom . The family of separation axioms so obtained is shown to include all the standard axioms T0, T1, …, T5, while familiar properties such as hyperconnectedness and ultraconnectedness are among the class of connectedness conditions. The regularity conditions include R0, R1, and regularity itself.

scholarly journals A note on the comparison of topologies

2001 ◽  
Vol 26 (4) ◽  
pp. 233-237
Author(s):  
Martin M. Kovár
Keyword(s):  
Separation Axiom ◽  
Covering Properties ◽  
Considerable Problem ◽  
Hausdorff Separation

A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is RR-pairwise paracompact, its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiomτS2σwhich is appropriate for the study of the bitopological collapse. We also show that the property that may cause the collapse is much weaker than some modifications of pairwise paracompactness and we generalize several results of T. G. Raghavan and I. L. Reilly (1977) regarding the comparison of topologies.

Pointwise Compact Spaces

1973 ◽  
Vol 16 (4) ◽  
pp. 545-549 ◽  
Author(s):  
Pedro Morales
Keyword(s):  
Topological Spaces ◽  
Locally Compact ◽  
Separation Axiom ◽  
Compact Spaces

In 1962, J. M. G. Fell [5] indicated the important role played by certain topological spaces which, though locally compact in a specialized sense, do not, in general, satisfy even the weakest separation axiom. He called them "locally compact". These were called "punktal kompakt" by Flachsmeyer [6] and to avoid confusion, we shall call them pointwise compact spaces.

scholarly journals On certain types of sets in ideal topological spaces

2015 ◽  
Vol 53 (2) ◽  
pp. 99-108
Author(s):  
Dhananjoy Mandal ◽  
M. N. Mukherjee
Keyword(s):  
Topological Space ◽  
Present Article ◽  
Topological Spaces ◽  
Separation Axiom

Abstract In the present article we introduce certain typical sets in an ideal topological space, some such corresponding versions in topological spaces being already there in the literature. We prove several properties of the introduced classes of sets, and finally as application, we initiate the study of a kind of separation axiom, termed $* - T_{{1 \over 2}}$ -property.

scholarly journals A Common Extension of Arhangel’skĭ’s Theorem and the Hajnal–Juhász Inequality

2020 ◽  
Vol 63 (1) ◽  
pp. 197-203 ◽  
Author(s):  
Angelo Bella ◽  
Santi Spadaro
Keyword(s):  
Hausdorff Space ◽  
Topological Spaces ◽  
Separation Axiom ◽  
Cardinal Invariants ◽  
Common Extension ◽  
Weak Lindelöf Number ◽  
Lindelöf Number

AbstractWe present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s solution to Alexandroff’s problem: A survey, Topology Appl. 153(2006), 2199–2217).In contrast to previous attempts, we do not need any separation axiom beyond $T_{2}$.

Fully admissible binary relations in topology

1977 ◽  
Vol 82 (2) ◽  
pp. 259-264
Author(s):  
D. M. G. McSherry
Keyword(s):  
Binary Relation ◽  
Continuous Mapping ◽  
Binary Relations ◽  
Separation Axiom

A fully admissible binary relation (3) is an operator , other than the equality operator and universal operator , which assigns to each space |S, τ|, a reflexive, symmetric, binary relation , and which is such that for any continuous mapping implies . With each such relation , we associate a ‘separation axiom’ , as well as ‘-regularity’ and ‘-connectedness’, where ≡ -regularity + T0, and -regularity + -connectedness ≡ indiscreteness.

SOME PROPERLY HEREDITARY BITOPOLOGICAL PROPERTIES

2021 ◽  
Vol 3 (1) ◽  
pp. 9-15
Author(s):  
B. Alkasasbeh ◽  
H. Hdeib
Keyword(s):  
Separation Axiom ◽  
Hereditary Properties

In this paper we discuss some pairwise properly hereditary properties concerning pairwise separation axiom, and obtain several results related to these properties.

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