Gutman A.E. Ordered locally convex spaces (11 publications, 2015

Gutman A.E.
Ordered locally convex spaces
11 publications, 2015–2024

Description of locally convex spaces which include nonclosed Archimedean cones; study of maximal cones in vector spaces

The notion of Archimedean convex set is introduced and studied.
It is shown that every locally convex space of uncountable dimension includes a nonclosed Archimedean cone.
It is proven that existence of a nonclosed linearly independent set implies existence of a nonclosed Archimedean cone.
An example is constructed of a countably-dimensioned locally convex space which admits discontinuous linear functionals but has no nonclosed linearly independent subsets.
A criterion is provided for a wedge to be Archimedean which is based on the notion of incoming direction.
The question is answered of when a wedge is included in a half-space.
The notion of (pre)lexicographic structure on a vector space is introduced and studied.
A new proof is presented for the theorem on isomorphic embedding of a totally ordered vector space into a lexicographically ordered space of real-valued functions with well-ordered supports.
A criterion is obtained for denseness of a maximal cone with respect to the strongest locally convex topology.
The class is characterized of vector spaces in which there exist nonbasic maximal cones.
The notion is introduced and studied of quasidense subset in a locally convex space.
An exhaustive description is provided for the class of locally convex spaces in which all Archimedean cones are closed.
Criteria are established for the closedness of Archimedean cones in countable-dimensional locally convex spaces in terms of projective parallelotopes and projective automorphisms.

List in BibTeX format

The papers are presented here for academic purposes and are not intended for mass dissemination or copying.

Last updated
March 22, 2024

1.	Gutman A.E. The problem of existence of nonclosed Archimedean cones [in Russian] // Report abstract. Geometry Days in Novosibirsk – 2015. International conference (Novosibirsk, August 26–29, 2015): Proceedings. Novosibirsk: Sobolev Institute of Mathematics SB RAS, 2015. P. 91–92. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
2.	Gutman A.E., Emelyanov E.Yu., Matyukhin A.V. Nonclosed Archimedean cones in locally convex spaces [in Russian] // Vladikavk. Math. J. 2015. V. 17, issue 3. P. 36–43. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate DOI resolution Journal site
3.	Gutman A.E., Matyukhin A.V. The problem of describing the locally convex spaces which include nonclosed Archimedean cones [in Russian] // Report abstract. Actual Questions of Contemporary Science. International scientific conference (Moscow, September 14–15, 2015): Proceedings. Moscow: RusAlliance Owl, 2015. P. 8–12. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Information on ResearchGate Abstracts on the site (Google Books)
4.	Gutman A.E., Matyukhin A.V. Topological vector spaces with nonclosed Archimedean cones [in Russian] // Prospero. 2015. V. 8, N 20. P. 62–64. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Journal issue (PDF) Information on ResearchGate Issue on the journal site (PDF) Issue table of content on the site (PDF) Journal site
5.	Gutman A.E., Matyukhin A.V. Nonclosed Archimedean cones [in Russian] // Report abstract. Geometry Days in Novosibirsk – 2016. International conference (Novosibirsk, September 21–24, 2016): Proceedings. Novosibirsk: Institute of Mathematics, 2016. P. 46–47. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
6.	Gutman A.E., Matyukhin A.V. Nonclosed Archimedean cones // Report abstract. Geometric Analysis and Control Theory. International conference (Novosibirsk, December, 8–12, 2016): Proceedings. Novosibirsk: Sobolev Institute of Mathematics SB RAS, 2016. P. 42–44. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
7.	Gutman A.E., Matyukhin A.V. Archimedean cones and incoming directions [in Russian] // Report abstract. Mathematics in the Modern World. International conference dedicated to the 60th anniversary of the Sobolev Institute of Mathematics (Novosibirsk, August 14–19, 2017): Proceedings. Novosibirsk: Institute of Mathematics, 2017. P. 154. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
8.	Gutman A.E. Archimedean and directionally closed cones // Report abstract. Geometry Days in Novosibirsk – 2018. International conference (Novosibirsk, September 19–22, 2018): Proceedings. Novosibirsk: Institute of Mathematics, 2018. P. 15. Bibliographic record Record in BibTeX format Report abstract (PDF) Cover (PDF) Abstracts (PDF) Conference program (PDF) Russian version (PDF) Information on ResearchGate Abstracts on the site (PDF) Program on the conference site (PDF) Conference site
9.	Gutman A.E., Emelianenkov I.A. Lexicographic structures on vector spaces [in Russian] // Vladikavk. Math. J. 2019. V. 21, issue 4. P. 42–55. Bibliographic record Record in BibTeX format Article (PDF) Prepublication version (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate DOI resolution Journal site
10.	Gutman A.E., Emelianenkov I.A. Locally convex spaces with all Archimedean cones closed [in Russian] // Sib. Matem. Zh. 2023. V. 64, N 5. P. 945–970. Bibliographic record Record in BibTeX format Article (PDF) Information on ResearchGate DOI resolution Journal site English version
	Gutman A.E., Emelianenkov I.A. Locally convex spaces with all Archimedean cones closed // Sib. Math. J. 2023. V. 64, N 5. P. 1117–1136. Bibliographic record Record in BibTeX format Article (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version
11.	Gutman A.E., Emelianenkov I.A. Quasidenseness in Rᴺ and projective parallelotopes [in Russian] // Sib. Matem. Zh. 2024. V. 65, N 2. P. 258–276. Bibliographic record Record in BibTeX format Article (PDF) Information on ResearchGate DOI resolution Journal site English version
	Gutman A.E., Emelianenkov I.A. Quasidenseness in Rᴺ and projective parallelotopes // Sib. Math. J. 2024. V. 65, N 2. P. 265–278. Bibliographic record Record in BibTeX format Article (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version

Gutman A.E.Ordered locally convex spaces11 publications, 2015–2024

Gutman A.E.
Ordered locally convex spaces
11 publications, 2015–2024