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Almost continuity implies closure continuity. (English) Zbl 0898.54015

Summary: The purpose of this note is to answer in the affirmative a long standing open question raised by M. K. Singal and A. R. Singal [Yokohama Math. J. 16, 63-73 (1968; Zbl 0191.20802)] – whether every almost continuous function is closure continuous (\(\theta\)-continuous).

MSC:

54C08 Weak and generalized continuity

Citations:

Zbl 0191.20802
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References:

[1] DOI: 10.2307/2039973 · Zbl 0313.54009
[2] Fomin, C. R. Dokl. Akad. Sci. URSS 32 pp 114– (1941)
[3] DOI: 10.2307/2313990 · Zbl 0145.19404
[4] Alexandroff, Verh. Nederl. Akad. Wetensch. Afd. Natuurk. Sect. l 14 pp 1– (1929)
[5] DOI: 10.2307/2036723 · Zbl 0186.56003
[6] Singal, Boll. Un. Mat. Ital. 4 pp 702– (1969)
[7] DOI: 10.2307/1994440 · Zbl 0151.30001
[8] DOI: 10.2307/2040493 · Zbl 0294.54013
[9] DOI: 10.2307/2039301 · Zbl 0261.54007
[10] Singal, Yokohama Math. J. 16 pp 63– (1968)
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