scholarly journals PRODUCTS OF BASE-κ-PARACOMPACT SPACES AND COMPACT SPACES

2011 ◽  
Vol 84 (3) ◽  
pp. 387-392
Author(s):  
LEI MOU
Keyword(s):  
Compact Spaces ◽  
Paracompact Spaces ◽  
Regular Ordinal

AbstractLet λ be a regular ordinal with λ≥ω1. Then we prove that (λ+1)×λ is not base-countably metacompact. This implies that base-κ-paracompactness is not an inverse invariant of perfect mappings, which answers a question asked by Yamazaki.

scholarly journals Characterizations of Strongly Paracompact Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Xin Zhang
Keyword(s):  
Open Cover ◽  
Normal Space ◽  
Compact Spaces ◽  
Countably Paracompact ◽  
Star Countable ◽  
Perfectly Normal Space ◽  
Paracompact Spaces ◽  
Perfectly Normal

Characterizations of strongly compact spaces are given based on the existence of a star-countable open refinement for every increasing open cover. It is proved that a countably paracompact normal space (a perfectly normal space or a monotonically normal space) is strongly paracompact if and only if every increasing open cover of the space has a star-countable open refinement. Moreover, it is shown that a space is linearlyDprovided that every increasing open cover of the space has a point-countable open refinement.

scholarly journals Normality Versus Paracompactness in Locally Compact Spaces

2018 ◽  
Vol 70 (1) ◽  
pp. 74-96 ◽  
Author(s):  
Alan Dow ◽  
Franklin D. Tall
Keyword(s):  
Strong Form ◽  
Locally Compact ◽  
Compact Spaces ◽  
Correct Proof ◽  
Chang’S Conjecture ◽  
Collectionwise Hausdorff ◽  
Chang's Conjecture ◽  
Paracompact Spaces ◽  
Locally Compact Spaces

AbstractThis note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the non-stationary ideal on ω1, as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the consistent characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of ω1.

On Simply* Compact Spaces

2019 ◽  
Vol 26 (4) ◽  
pp. 196-200
Keyword(s):  
Compact Spaces

On Simply* Compact Spaces

2019 ◽  
Vol 264 (1) ◽  
pp. 196-200
Keyword(s):  
Compact Spaces

A note on monotonically star $\sigma$-compact spaces

2019 ◽  
Vol 26 (4) ◽  
pp. 527-534
Author(s):  
Yan-Kui Song ◽  
Wei-Feng Xuan
Keyword(s):  
Compact Spaces

Soft pre seperation axioms and soft pre compact spaces

2020 ◽  
pp. 549-559
Author(s):  
M. Ravindran ◽  
B. Arun ◽  
G. Ilango
Keyword(s):  
Compact Spaces

In this paper soft pre separations are defined and few of their properties are stated and proved. Also soft pre compactness is defined and properties of a such a space are discussed.

On 𝒞ℛ-Epic Embeddings and Absolute 𝒞ℛ-Epic Spaces

2005 ◽  
Vol 57 (6) ◽  
pp. 1121-1138 ◽  
Author(s):  
Michael Barr ◽  
R. Raphael ◽  
R. G. Woods
Keyword(s):  
Locally Compact ◽  
Compact Spaces ◽  
Open Questions ◽  
Tychonoff Spaces ◽  
Locally Compact Spaces

AbstractWe study Tychonoff spaces X with the property that, for all topological embeddings X → Y, the induced map C(Y ) → C(X) is an epimorphism of rings. Such spaces are called absolute 𝒞ℛ-epic. The simplest examples of absolute 𝒞ℛ-epic spaces are σ-compact locally compact spaces and Lindelöf P-spaces. We show that absolute CR-epic first countable spaces must be locally compact.However, a “bad” class of absolute CR-epic spaces is exhibited whose pathology settles, in the negative, a number of open questions. Spaces which are not absolute CR-epic abound, and some are presented.

scholarly journals nIαg-Compact spaces and nIαg-Lindelof spaces in nano ideal topological spaces

2020 ◽  
Author(s):  
M. Parimala ◽  
D. Arivuoli ◽  
R. Perumal ◽  
S. Krithika
Keyword(s):  
Topological Spaces ◽  
Compact Spaces

On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups

2003 ◽  
Vol 10 (2) ◽  
pp. 209-222
Author(s):  
I. Bakhia
Keyword(s):  
Wide Class ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Topological Groups ◽  
Compact Spaces ◽  
Topological Semigroups

Abstract Functions of dimension modulo a (rather wide) class of spaces are considered and the conditions are found, under which the dimension of the product of spaces modulo these classes is equal to zero. Based on these results, the sufficient conditions are established, under which spaces of free topological semigroups (in the sense of Marxen) and spaces of free topological groups (in the sense of Markov and Graev) are zero-dimensional modulo classes of compact spaces.

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