scholarly journals C-normal topological property

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 407-411 ◽  
Author(s):  
Samirah AlZahrani ◽  
Lutfi Kalantan
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Normal Space ◽  
Compact Subspace ◽  
Bijective Function

A topological space X is called C-normal if there exist a normal space Y and a bijective function f : X ? Y such that the restriction f _ C : C ? f (C) is a homeomorphism for each compact subspace C ? X. We investigate this property and present some examples to illustrate the relationships between C-normality and other weaker kinds of normality.

scholarly journals P-Normality

2021 ◽  
Vol 12 (6) ◽  
pp. 1-8
Author(s):  
LUTFI KALANTAN ◽  
MAI MANSOURI
Keyword(s):  
Topological Space ◽  
Normal Space ◽  
Bijective Function

A topological space X is called P-normal if there exist a normal space Y and a bijective function f : X −→ Y such that the restriction f|A : A −→ f(A) is a homeomorphism for each paracompact subspace A ⊆ X. We will investigate this property and produce some examples to illustrate the relation between P-normality and other weaker kinds of normality.

scholarly journals Results on C2-paracompactness

2021 ◽  
Vol 14 (2) ◽  
pp. 351-357
Author(s):  
Hala Alzumi ◽  
Lutfi Kalantan ◽  
Maha Mohammed Saeed
Keyword(s):  
Topological Space ◽  
Paracompact Space ◽  
Compact Subspace ◽  
Bijective Function

A C-paracompact is a topological space X associated with a paracompact space Y and a bijective function f : X −→ Y satisfying that f A: A −→ f(A) is a homeomorphism for each compact subspace A ⊆ X. Furthermore, X is called C2-paracompact if Y is T2 paracompact. In this article, we discuss the above concepts and answer the problem of Arhangel’ski ̆i. Moreover, we prove that the sigma product Σ(0) can not be condensed onto a T2 paracompact space.

Separable Topological Space of Hereditary

NUTA Journal ◽  
2020 ◽  
Vol 7 (1-2) ◽  
pp. 68-70
Author(s):  
Raj Narayan Yadav ◽  
Bed Prasad Regmi ◽  
Surendra Raj Pathak
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Sufficient Condition ◽  
Topological Properties ◽  
Necessary And Sufficient Condition ◽  
Separable Space ◽  
Separable Topological Space ◽  
Necessary And Sufficient

A property of a topological space is termed hereditary ifand only if every subspace of a space with the property also has the property. The purpose of this article is to prove that the topological property of separable space is hereditary. In this paper we determine some topological properties which are hereditary and investigate necessary and sufficient condition functions for sub-spaces to possess properties of sub-spaces which are not in general hereditary.

On Certain Onto Maps

1962 ◽  
Vol 14 ◽  
pp. 461-466 ◽  
Author(s):  
Isaac Namioka
Keyword(s):  
Topological Space ◽  
Closed Subspace ◽  
Dimensional Space ◽  
Extension Theorem ◽  
Normal Space ◽  
Continuous Map ◽  
Image Position

Let Δn (n > 0) denote the subset of the Euclidean (n + 1)-dimensional space defined byA subset σ of Δn is called a face if there exists a sequence 0 ≤ i1 ≤ i2 ≤ … < im ≤ n such thatand the dimension of σ is defined to be (n — m). Let denote the union of all faces of Δn of dimensions less than n. A topological space Y is called solid if any continuous map on a closed subspace A of a normal space X into Y can be extended to a map on X into Y. By Tietz's extension theorem, each face of Δn is solid. The present paper is concerned with a generalization of the following theorem which seems well known.

scholarly journals On normal subspaces

1981 ◽  
Vol 23 (1) ◽  
pp. 1-4
Author(s):  
D.B. Gauld ◽  
I.L. Reilly ◽  
M.K. Vamanamurthy
Keyword(s):  
Topological Space ◽  
Normal Space

In this paper the anti-normal property is studied. A space is anti-normal if its only normal subspaces are those whose cardinalities require them to be normal. It is shown that every topological space of at least four elements contains a normal three point subspace from which it follows that there is only one non-trivial anti-normal space.

scholarly journals On Completely Normal Spaces

2019 ◽  
Vol 24 (5) ◽  
pp. 111
Author(s):  
Taha H. Jasim1 ◽  
Luma H. Othman
Keyword(s):  
Topological Property ◽  
Normal Space ◽  
Hereditary Property ◽  
New Class ◽  
The Subject ◽  
The Relationship

The purpose of this paper is to introduce a new class of completely normal spaces namely , ) completely normal space . The relationship between them was studied and we investigate some characterizations of them. At last we give more of examples to explain the subject and study the topological property and hereditary property of these types.   http://dx.doi.org/10.25130/tjps.24.2019.099

scholarly journals LINEARLY ORDERED SPACE WHOSE SQUARE AND HIGHER POWERS CANNOT BE CONDENSED ONTO A NORMAL SPACE

2017 ◽  
Vol 20 (10) ◽  
pp. 68-73
Author(s):  
O.I. Pavlov
Keyword(s):  
Topological Space ◽  
Normal Space ◽  
Topological Properties ◽  
Pseudocompact Spaces ◽  
Countably Compact ◽  
Ordered Space ◽  
One To One ◽  
Hereditary Properties

One of the central tasks in the theory of condensations is to describe topological properties that can be improved by condensation (i.e. a continuous one-to-one mapping). Most of the known counterexamples in the field deal with non-hereditary properties. We construct a countably compact linearly ordered (hence, monotonically normal, thus ” very strongly” hereditarily normal) topological space whose square and higher powers cannot be condensed onto a normal space. The constructed space is necessarily pseudocompact in all the powers, which complements a known result on condensations of non-pseudocompact spaces.

scholarly journals C-Tychonoff and L-Tychonoff Topological Spaces

2018 ◽  
Vol 11 (3) ◽  
pp. 882-892 ◽  
Author(s):  
Samirah ALZahrani
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Tychonoff Space ◽  
Local Compactness ◽  
Compact Subspace ◽  
One To One

A topological space X is called C-Tychonoff if there exist a one-to-one function f from X onto a Tychonoff space Y such that f restriction K from K onto f(K) is a homeomorphism for each compact subspace K of X. We discuss this property and illustrate the relationships between C-Tychonoffness and some other properties like submetrizability, local compactness, L-Tychononess, C-normality, C-regularity, epinormality, sigma-compactness, pseudocompactness and zero-dimensional.

RNA Shape Space Topology

2000 ◽  
Vol 6 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Jan Cupal ◽  
Stephan Kopp ◽  
Peter F. Stadler
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Secondary Structures ◽  
Shape Space ◽  
Rna Secondary Structures ◽  
Theory Of Evolution ◽  
Space Topology ◽  
Evolutionary Trajectories ◽  
Phenotype Space ◽  
Standing Problem

The distinction between continuous and discontinuous transitions is a long-standing problem in the theory of evolution. Because continuity is a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the probabilities with which one phenotype is accessible from another through changes at the genotypic level. The shape space of RNA secondary structures is used to illustrate this approach. We show that evolutionary trajectories are continuous if and only if they follow connected paths in phenotype space.

Even Covering Properties and Somewhat Normal Spaces

1986 ◽  
Vol 29 (2) ◽  
pp. 154-159
Author(s):  
Hans-Peter Künzi ◽  
Peter Fletcher
Keyword(s):  
Topological Space ◽  
Open Cover ◽  
Normal Space ◽  
Completely Regular ◽  
Covering Properties ◽  
Normal Cover

AbstractA topological space X is said to be somewhat normal provided that for each open cover is a normal cover of X. We show that a completely regular somewhat normal space need not be normal, thereby answering a question of W. M. Fleischman. We note that a collectionwise normal somewhat normal space need not be almost 2-fully normal, as had previously been asserted, and that neither the perfect image nor the perfect preimage of a somewhat normal space has to be somewhat normal.

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