scholarly journals A class of spaces containing all generalized absolutely closed (almost compact) spaces

2006 ◽  
Vol 7 (2) ◽  
pp. 233 ◽  
Author(s):  
J.K. Kohli ◽  
A.K. Das
Keyword(s):  
Compact Spaces ◽  
Absolutely Closed

scholarly journals The completion of a topological group

1980 ◽  
Vol 21 (3) ◽  
pp. 407-417 ◽  
Author(s):  
Eric C. Nummela
Keyword(s):  
Topological Group ◽  
Topological Spaces ◽  
Topological Groups ◽  
Russian School ◽  
Compact Spaces ◽  
French School ◽  
Absolutely Closed

During the 1920's and 30's, two distinct theories of “completions” for topological spaces were being developed: the French school of mathematics was describing the familiar notion of “complete relative to a uniformity”, and the Russian school the less well-known idea of “absolutely closed”. The two agree precisely for compact spaces.The first part of this article describes these two notions of completeness; the remainder is a presentation of the interesting, but apparently unrecorded, fact that the two ideas coincide when put in the context of topological groups.

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.

scholarly journals Several results on compact metrizable spaces in $$\mathbf {ZF}$$

2021 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch
Keyword(s):  
Continuum Hypothesis ◽  
Compact Spaces ◽  
Power Set ◽  
Compact Metrizable Space ◽  
Permutation Models ◽  
Independence Results ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Transfer Theorems ◽  
The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

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