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Keywords:
pseudo-radial spaces; prime spaces; sub pseudo-radial spaces; tightness; Martin's Axiom
pseudo-radial spaces; prime spaces; sub pseudo-radial spaces; tightness; Martin's Axiom
Summary:
It is proved that, under the Martin's Axiom, every $T_1$-space with countable tightness is a subspace of some pseudo-radial space. We also give several characterizations of subspaces of pseudo-radial spaces and conclude that being a subspace of a pseudo-radial space is a local property.
References:
[1] Arhangel'skii A.V., Isler R., Tironi G.: On pseudo-radial spaces. Comment. Math. Univ. Carolinae 27 (1986), 137-154. MR 0843426
[2] Tironi G.: Some remarks on radial and pseudo-radial spaces. in: Proceedings of the Fifth Topological Symposium 1981, ed. by J. Novák, pp. 608-612. MR 0698465 | Zbl 0492.54003
[3] Franklin S.P., Rajagopalan M.: On subsequential spaces. Topology Appl. 35 (1990), 1-19. MR 1049858 | Zbl 0722.54021
[4] Fremlin D.H.: Consequences of Martin's Axiom. Cambridge Tracts in Mathematics, Cambridge, 1984. Zbl 1156.03050
[5] Jane I., Meyer P.R., Simon P., Wilson P.G.: On tightness in chain-net spaces. Comment. Math. Univ. Carolinae 22 (1981), 809-817. MR 0647028 | Zbl 0485.54003
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