Proper actions on topological groups: Applications to quotient spaces

AbstractIn this paper, we continue the study of s-topological and irresolute-topological groups. We define semi-quotient mappings which are stronger than semi-continuous mappings, and then consider semi-quotient spaces and groups. It is proved that for some classes of irresolute-topological groups (G, *, τ) the semi-quotient space G/H is regular. Semi-isomorphisms of s-topological groups are also discussed.

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Cellularity in quotient spaces of topological groups

Forum Mathematicum ◽

10.1515/forum-2018-0195 ◽

2019 ◽

Vol 31 (2) ◽

pp. 351-359

Author(s):

Mikhail G. Tkachenko

Keyword(s):

Topological Group ◽

Quotient Space ◽

Compact Subgroup ◽

Topological Groups ◽

Quotient Spaces

AbstractLet G be an arbitrary topological group. We prove that the cellularity of G is equal to the cellularity of the quotient space {G/K} for every compact subgroup K of G.

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SOME PROPERTIES OF G-SPACES ACTED WITH TOPOLOGICAL GROUPS

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.7.56 ◽

2020 ◽

Vol 9 (7) ◽

pp. 4917-4922

Author(s):

S. Sivakumar ◽

D. Lohanayaki

Keyword(s):

Topological Groups

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Homomorphisms of topological groups that cannot be factorized by weight and dimension

Mathematical Notes ◽

10.1007/bf01158253 ◽

1987 ◽

Vol 41 (3) ◽

pp. 226-228

Author(s):

V. G. Pestov

Keyword(s):

Topological Groups

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CONTINUITY OF MEASURABLE HOMOMORPHISMS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972708000610 ◽

2008 ◽

Vol 78 (1) ◽

pp. 171-176 ◽

Cited By ~ 2

Author(s):

JANUSZ BRZDȨK

Keyword(s):

Topological Group ◽

Abelian Group ◽

Baire Property ◽

Topological Groups ◽

Locally Compact ◽

Compact Topological Group ◽

Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

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Achieving a Sustainable Development Process by Deployment of Solar PV Power in ASEAN: A SWOT Analysis

Processes ◽

10.3390/pr9040630 ◽

2021 ◽

Vol 9 (4) ◽

pp. 630

Author(s):

Hengtian Wang ◽

Xiaolong Yang ◽

Qihe Lou ◽

Xinxin Xu

Keyword(s):

Sustainable Development ◽

Development Process ◽

Swot Analysis ◽

Primary Energy ◽

Solar Pv ◽

Proper Actions ◽

External Threats ◽

Process Deployment ◽

Asean Countries ◽

Primary Energy Supply

The Association of Southeast Asian Nations (ASEAN) has experienced rapid social and economic development in the past decades, while energy shortage, environmental pollution, and climate change are the factors that prevent a sustainable development process. Deployment of solar photovoltaic (PV) power is one of the effective alternatives to overcome the above barriers and assist ASEAN to achieve the aspirational target of 23% renewable energy (RE) in the total primary energy supply (TPES). In this study, SWOT analysis is adopted to analyze the internal strengths and weaknesses and the external threats and opportunities tightly related to the development of solar PV power in ASEAN countries. Through the SWOT analysis, great potential for the development of solar PV power in ASEAN is found. As long as appropriate policies are implemented and proper actions are taken, huge space for deployment of solar PV power can be expected. Based on the SWOT analysis, countermeasures that emphasize further deployment of solar PV power in ASEAN countries are put forward. The tactics include arousing people’s awareness of a sustainable development process, government issue coherence and stable incentive policies, fostering a solar PV industry chain and master key technology, and seek opportunities via an international cooperation.

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

Georgian Mathematical Journal ◽

10.1515/gmj.2003.209 ◽

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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PROPER ACTIONS ON SOME EXPONENTIAL SOLVABLE HOMOGENEOUS SPACES

International Journal of Mathematics ◽

10.1142/s0129167x0500317x ◽

2005 ◽

Vol 16 (09) ◽

pp. 941-955 ◽

Cited By ~ 12

Author(s):

ALI BAKLOUTI ◽

FATMA KHLIF

Keyword(s):

Maximal Subgroup ◽

Homogeneous Space ◽

Lie Group ◽

Homogeneous Spaces ◽

Intersection Property ◽

Nilpotent Lie Group ◽

Proper Actions ◽

Simply Connected

Let G be a connected, simply connected nilpotent Lie group, H and K be connected subgroups of G. We show in this paper that the action of K on X = G/H is proper if and only if the triple (G,H,K) has the compact intersection property in both cases where G is at most three-step and where G is special, extending then earlier cases. The result is also proved for exponential homogeneous space on which acts a maximal subgroup.

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