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  • The active participants of the seminar were discuss new results and posed some open problems.

• Divertisement
  • The active participants of the seminar were discuss new results and posed some open problems.

• On nontopologized groups
  • The reporter discusses on the construction of a non-topologized group and related topics.

• On the monoid of cofinite monotone partial bijections of nx_lexZ
  • The reporter discusses on the lattice of congruences of the monoid of cofinite monotone partial bijections of nx_lexZ.

• Pseudocompact primitive topological inverse semigroups
  • In the report we discuss on pseudocompact primitive topological inverse semigroups. We describe the structure of pseudocompact primitive topological inverse semigroups and show that a Tychonoff product of a family of pseudocompact primitive topological inverse semigroups is a pseudocompact topological space. Also we prove that the Stone-\v{C}ech compactification of a pseudocompact primitive topological inverse semigroup is a compact primitive topological inverse semigroup.

• On semitopological semigroup C
  • In the report we discuss on embeddings of the semigroup C=< a,b | a² b=a, ab ² =b> into compact-like topological (semitopological) semigroups.

• Divertisement
  • The active participants of the seminar were discuss new results and posed some open problems.

• Different classes of bounded topological groups
  • Following the problems of I. Yo. Guran from the previous seminar, we impose different bound conditions on topological groups. We are trying to distinguish these conditions in different classes of topological groups and formulate new problems.

• On continuity of group operations
  • Based on speaker's PhD thesis we start a cycle of lectures devoted to continuity of group operations in paratopological and semitopological groups, with an accent on game based proofs having in mind to apply them for proving that some inverse topological semigroups are topological inverse semigroups.

• On continuity of group operations, II
  • Based on speaker's PhD thesis we start a cycle of lectures devoted to continuity of group operations in paratopological and semitopological groups, with an accent on game based proofs having in mind to apply them for proving that some inverse topological semigroups are topological inverse semigroups.
    We shall continue the survey. In particular: We shall consider when a paratopological group is a topological group; we recall related S-spaces introduced by E. Reznichenko. We shall consider when a semitopological group G is a paratopological group; we shall deal with topological games and recall the positive Reznichenko's when (G,G) is a Grothendieck pair. We shall consider when a cancellative topological semigroup is a group: we shall recall Artur Hideyuki Tomita's result that for initially \omega_1-compact semigroups the solution if the problem is independent of (ZFC+\frak c=\omega_2).

• On continuity of group operations, III
  • Based on speaker's PhD thesis we start a cycle of lectures devoted to continuity of group operations in paratopological and semitopological groups, with an accent on game based proofs having in mind to apply them for proving that some inverse topological semigroups are topological inverse semigroups.
    We shall continue the survey. In particular: We shall consider when a semitopological group G is a paratopological group; we shall deal with topological games and recall the positive Reznichenko's when (G,G) is a Grothendieck pair. We shall consider when a cancellative topological semigroup is a group: we shall recall Artur Hideyuki Tomita's result that for initially \omega_1-compact semigroups the solution if the problem is independent of (ZFC+\frak c=\omega_2).

• Pseudocompactness is 3-space property for paratopological groups
  • The speaker wishes to devote a couple of talks to his proof that a paratopological group G is pseudocompact provided G has a normal subgroup N such that both N and the quotient paratopological group G/N are pseudocompact. Remark: The result was obtained by the speaker during the last week and it positively solves more than 3/2 problems from the survey by Michail Tkachenko. So the listeners of the seminar will have the unique occasion to be the first persons in the world who will hear the solution. Acknowledgement: The speaker wishes to thank to Oleg Gutik who invited him for the talks.

• Group actions and the Brandt λ⁰-extensions of monoids with zero
  • We establish isomorphisms of the Brandt λ⁰-extensions of monoids with zeros and describe a category whose objects are ingredients in the constructions of the Brandt λ⁰-extensions of monoids with zeros and morphisms are isomorphisms of so extensions.

• On adjoining zero to a paratopological group and preserving pseudocompactness by products in some classes of (semi)topological semigroups
  • We discuss the topics presented in the title of the report.

• Means on scattered compacta
  • We shall prove that a separable scattered compact space containing a cocountable subset homeomorphic to [0, ω₁] admits no separately continuous mean and no diagonally continuous n-mean for n ≥ 2.