• Korean Journal of Mathematics
• /
• v.29 no.3
• /
• pp.555-561
• /
• 2021

In this paper, we investigate some properties of countably g-compact and sequentially GO-compact spaces. Also, we discuss the relation between countably g-compact and sequentially GO-compact. Next, we introduce the definition of g-subspace and study the characterization of g-subspace.

• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.297-303
• /
• 2007

In this paper, we study on C-closed spaces, SC-closed spaces and related spaces. We show that a sequentially compact SC-closed space is sequential and as corollaries obtain that a sequentially compact space with unique sequential limits is sequential if and only if it is C-closed [7, 1.19 Proposition] and every sequentially compact SC-closed space is C-closed. We also show that a countably compact WAP and C-closed space is sequential and obtain that a countably compact (or compact or sequentially compact) WAP-space with unique sequential limits is sequential if and only if it is C-closed as a corollary. Finally we prove that a weakly discretely generated AP-space is C-closed. We then obtain that every countably compact (or compact or sequentially compact) weakly discretely generated AP-space is $Fr\acute{e}chet$-Urysohn with unique sequential limits, for weakly discretely generated AP-spaces, unique sequential limits ${\equiv}KC{\equiv}C-closed{\equiv}SC-closed$, and every continuous surjective function from a countably compact (or compact or sequentially compact) space onto a weakly discretely generated AP-space is closed as corollaries.

• Communications of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.145-152
• /
• 2009

In this paper, we introduce a new property of a topological space which is weaker than sequential compactness and give some necessary and sufficient conditions for a $Fr{\acute{e}}chet$-Urysohn space with the property to be sequentially compact.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.4
• /
• pp.929-942
• /
• 2023

In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(IFS) on uniform spaces. We show that an IFS on a sequentially compact uniform space with topological ergodic shadowing property has topological shadowing property. We define the notion of topological pseudo-orbital specification property and investigate its relation to topological ergodic shadowing property. We find that a topologically mixing IFS on a compact and sequentially compact uniform space with topological shadowing property has topological pseudo-orbital specification property and thus has topological ergodic shadowing property.

• Korean Journal of Mathematics
• /
• v.25 no.1
• /
• pp.61-70
• /
• 2017

In this paper, we introduce the concept of statistically sequentially quotient map which is a generalization of sequence covering map and discuss the relation with covering maps by some examples. Using this concept, we give an affirmative answer for a question by Fucai Lin and Shou Lin.

• Communications of the Korean Mathematical Society
• /
• v.25 no.3
• /
• pp.477-484
• /
• 2010

In this paper, we introduce a new property (*) of a topological space and prove that if X satisfies one of the following conditions (1) and (2), then compactness, countable compactness and sequential compactness are equivalent in X; (1) Each countably compact subspace of X with (*) is a sequential or AP space. (2) X is a sequential or AP space with (*).

• Honam Mathematical Journal
• /
• v.26 no.2
• /
• pp.209-218
• /
• 2004

On the analogy of total countable compactness, we study interesting subfamilies in the class of pseudocompact spaces. We show relationships between totally pseudocompact spaces, sequentially pseudocompact spaces, and DFCC spaces. We also prove relationships among densely ${\xi}$-pseudocompact, ${\xi}$-pseudocompact, and countably pracompact spaces. As a productive result on countably pracompact spaces, we will prove that if X is a countably pracompact space and Y is a countably pracompact ${\kappa}$-space, then $X{\times}Y$ is count ably pracompact.

• Journal of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.261-273
• /
• 2007

In this paper, we introduce some new properties of a topological space which are respectively generalizations of $Fr\'{e}chet$-Urysohn property. We show that countably AP property is a sufficient condition for a space being countable tightness, sequential, weakly first countable and symmetrizable, to be ACP, $Fr\'{e}chet-Urysohn$, first countable and semimetrizable, respectively. We also prove that countable compactness is a sufficient condition for a countably AP space to be countably $Fr\'{e}chet-Urysohn$. We then show that a countably compact space satisfying one of the properties mentioned here is sequentially compact. And we show that a countably compact and countably AP space is maximal countably compact if and only if it is $Fr\'{e}chet-Urysohn$. We finally obtain a sufficient condition for the ACP closure operator $[{\cdot}]_{ACP}$ to be a Kuratowski topological closure operator and related results.

• Current Optics and Photonics
• /
• v.3 no.3
• /
• pp.243-247
• /
• 2019

We have developed a compact, wavelength-selectable, Q-switched Nd:YAG laser at mid ultraviolet for chemical warfare agent detection. The fundamental wave at 1064 nm is delivered by a pulsed solid state laser incorporating with a square-type Nd:YAG rod in a resonator closed by two crossed Porro prisms for environmental reliability. The output energy at 213 nm ($5{\omega}$) and 266 nm ($4{\omega}$) by ${\chi}^{(2)}$ process in the sequentially disposed BBO crystals are measured to be 6.8 mJ and 15.1 mJ, respectively. The output wavelength is selected for $5{\omega}$ and $4{\omega}$ by a motorized wavelength switch. The energy ratio of the $5{\omega}$ to the $4{\omega}$ is varied from 0.05 to 0.85 by controlling the phase matching temperature of the nonlinear crystal for sum-frequency generation without change of the output pulse parameters.

• Honam Mathematical Journal
• /
• v.36 no.2
• /
• pp.425-434
• /
• 2014

In this paper, we introduce a new concept of a countably sequential space which is a generalization of a sequential space and study some properties of a countably sequential space and relations among the space and related spaces.