Some properties of 𝑘-semistratifiable spaces

Mizokami, T.

doi:10.1090/S0002-9939-1990-0990429-9

Some properties of $k$-semistratifiable spaces
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Proc. Amer. Math. Soc. 108 (1990), 535-539 Request permission

Abstract:

We study spaces admitting semistratification and $k$-semistratifications with (CF) property. The class of $k$-semistratifiable spaces with (CF) property lies between the class of Lašnev spaces and that of $k$-semistratifiable spaces, and really differs from the classes of stratifiable spaces and $\aleph$-spaces.

References

Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. MR 188982, DOI 10.2140/pjm.1966.17.1
Jack G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105–125. MR 131860, DOI 10.2140/pjm.1961.11.105
L. Foged, A characterization of closed images of metric spaces, Proc. Amer. Math. Soc. 95 (1985), no. 3, 487–490. MR 806093, DOI 10.1090/S0002-9939-1985-0806093-3
Gary Gruenhage, Generalized metric spaces, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 423–501. MR 776629
Shou Lin, A study of pseudobases, Questions Answers Gen. Topology 6 (1988), no. 1, 81–97. MR 940446
Shou Lin, On a problem of K. Tamano, Questions Answers Gen. Topology 6 (1988), no. 1, 99–102. MR 940447
Shou Lin, Mapping theorems on $\aleph$-spaces, Topology Appl. 30 (1988), no. 2, 159–164. MR 967752, DOI 10.1016/0166-8641(88)90014-4
D. J. Lutzer, Semimetrizable and stratifiable spaces, General Topology and Appl. 1 (1971), no. 1, 43–48. MR 296893, DOI 10.1016/0016-660X(71)90109-7
E. Michael, $\aleph _{0}$-spaces, J. Math. Mech. 15 (1966), 983–1002. MR 0206907
Takemi Mizokami, On CF families and hyperspaces of compact subsets, Topology Appl. 35 (1990), no. 1, 75–92. MR 1049863, DOI 10.1016/0166-8641(90)90122-I
Akihiro Okuyama, On a generalization of $\Sigma$-spaces, Pacific J. Math. 42 (1972), 485–495. MR 313995, DOI 10.2140/pjm.1972.42.485