scholarly journals Compact condensations of Hausdorff spaces

2021 ◽  
Author(s):  
V. I. Belugin ◽  
A. V. Osipov ◽  
E. G. Pytkeev
Keyword(s):  
Hausdorff Spaces

scholarly journals SUBPROJECTIVITY OF PROJECTIVE TENSOR PRODUCTS OF BANACH SPACES OF CONTINUOUS FUNCTIONS

2021 ◽  
pp. 1-14
Author(s):  
R.M. CAUSEY
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Tensor Products ◽  
Continuous Functions ◽  
Hausdorff Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Spaces Of Continuous Functions

Abstract Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is c0-saturated if and only if it is subprojective if and only if K and L are both scattered. We remove the hypothesis of metrizability from their result and extend it from the case of the twofold projective tensor product to the general n-fold projective tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff spaces K1, …, K n , $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is c0-saturated if and only if it is subprojective if and only if each K i is scattered.

scholarly journals On modal logics arising from scattered locally compact Hausdorff spaces

2019 ◽  
Vol 170 (5) ◽  
pp. 558-577
Author(s):  
Guram Bezhanishvili ◽  
Nick Bezhanishvili ◽  
Joel Lucero-Bryan ◽  
Jan van Mill
Keyword(s):  
Modal Logics ◽  
Hausdorff Spaces ◽  
Locally Compact

scholarly journals Two semigroups of continuous relations

1977 ◽  
Vol 23 (1) ◽  
pp. 46-58 ◽  
Author(s):  
A. R. Bednarek ◽  
Eugene M. Norris
Keyword(s):  
Large Class ◽  
Algebraic Structure ◽  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Completely Regular ◽  
Topological Semigroups ◽  
Stone Type

SynopsisIn this paper we define two semigroups of continuous relations on topological spaces and determine a large class of spaces for which Banach-Stone type theorems hold, i.e. spaces for which isomorphism of the semigroups implies homeomorphism of the spaces. This class includes all 0-dimensional Hausdorff spaces and all those completely regular Hausdorff spaces which contain an arc; indeed all of K. D. Magill's S*-spaces are included. Some of the algebraic structure of the semigroup of all continuous relations is elucidated and a method for producing examples of topological semigroups of relations is discussed.

scholarly journals Infinitary logic and basically disconnected compact Hausdorff spaces

2018 ◽  
Vol 28 (6) ◽  
pp. 1275-1292
Author(s):  
Antonio Di Nola ◽  
Serafina Lapenta ◽  
Ioana LeuŞtean
Keyword(s):  
Infinitary Logic ◽  
Hausdorff Spaces

scholarly journals On the cardinality of power homogeneous Hausdorff spaces

2006 ◽  
Vol 192 (3) ◽  
pp. 255-266 ◽  
Author(s):  
G. J. Ridderbos
Keyword(s):  
Hausdorff Spaces

scholarly journals Skew compact semigroups

2003 ◽  
Vol 4 (1) ◽  
pp. 133
Author(s):  
Ralph D. Kopperman ◽  
Desmond Robbie
Keyword(s):  
Continuous Semigroup ◽  
Minimal Ideal ◽  
Compact Semigroup ◽  
Closed Ideal ◽  
Hausdorff Spaces ◽  
Compact Spaces ◽  
Compact Semigroups ◽  
Compact Topology ◽  
Hausdorff Group ◽  
Non Hausdorff Spaces

<p>Skew compact spaces are the best behaving generalization of compact Hausdorff spaces to non-Hausdorff spaces. They are those (X ; τ ) such that there is another topology τ* on X for which τ V τ* is compact and (X; τ ; τ*) is pairwise Hausdorff; under these conditions, τ uniquely determines τ *, and (X; τ*) is also skew compact. Much of the theory of compact T<sub>2</sub> semigroups extends to this wider class. We show:</p> <p>A continuous skew compact semigroup is a semigroup with skew compact topology τ, such that the semigroup operation is continuous τ<sup>2</sup>→ τ. Each of these contains a unique minimal ideal which is an upper set with respect to the specialization order.</p> <p>A skew compact semigroup which is a continuous semigroup with respect to both topologies is called a de Groot semigroup. Given one of these, we show:</p> <p>It is a compact Hausdorff group if either the operation is cancellative, or there is a unique idempotent and S<sup>2</sup> = S.</p> <p>Its topology arises from its subinvariant quasimetrics.</p> <p>Each *-closed ideal ≠ S is contained in a proper open ideal.</p>

scholarly journals Two notes on ``On soft Hausdorff spaces"

2018 ◽  
Vol 16 (3) ◽  
pp. 333-336 ◽  
Author(s):  
M. E. El-Shafei ◽  
T. M. Al-shami ◽  
M. Abo-Elhamayel
Keyword(s):  
Hausdorff Spaces
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